Prvočísla a zložené čísla sú ako stavebné kamene matematiky! Každé... Show more
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Updated Mar 22, 2026
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Prvočísla a Zložené Čísla: Jednoduché Vysvetlenie
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Prvočísla a zložené čísla - základy
Matematika je vlastne ako stavebnica - a prvočísla sú jej najmenšie kocky! Sú to čísla, ktoré majú presne dva delitele: číslo 1 a samo seba. Napríklad 7 sa dá vydeliť len číslom 1 a 7.
Zložené čísla sú väčšie stavby z týchto kociek. Majú viac ako dva delitele. Číslo 6 napríklad môžeš vydeliť číslami 1, 2, 3 a 6 - to sú štyri delitele!
Číslo 1 je úplne špeciálne - nie je ani prvočíslo, ani zložené číslo. Má totiž len jeden deliteľ (seba samého), takže sa do žiadnej skupiny nehodí.
💡 Tip: Číslo 2 je jediné párne prvočíslo! Všetky ostatné párne čísla sú zložené, lebo sa dajú vydeliť aspoň číslom 2.
Ako rozoznáš prvočíslo od zlženého čísla
Zistiť typ čísla je ako detektívka - musíš nájsť všetkých jeho deliteľov! Začni vždy s číslom 1 a samotným číslom. Potom skúšaj menšie čísla ako 2, 3, 4, 5...
Pravidlá deliteľnosti ti ušetria veľa času. Ak je číslo párne, je deliteľné 2. Ak súčet jeho cifier je deliteľný 3, aj celé číslo je deliteľné 3. Končí na 0 alebo 5? Je deliteľné 5.
Príklad s číslom 17: Nie je párne, súčet cifier je 8 (nie deliteľný 3), nekončí na 0 ani 5. Skús ešte 7 - nevyjde ti to. Máš len deliteľov 1 a 17 = prvočíslo!
💡 Skvelá správa: Nemusíš skúšať všetky čísla! Stačí ísť len do odmocniny z daného čísla, ale zatiaľ sa sústredíme na menšie čísla.
Rozklad na súčin prvočísel - strom rozkladu
Tu prichádza to najzaujímavejšie! Každé zložené číslo sa dá rozložiť na súčin len prvočísel. Je to ako rozobratá stavebnica na základné kocky.
Strom rozkladu funguje takto: Začni s číslom, ktoré chceš rozložiť. Nájdi dva jeho delitele (okrem 1) a napíš ich pod neho. Spoj ich čiarkami.
Pre číslo 12: Začni s 12, rozlož na 2 × 6. Číslo 2 je prvočíslo (zakrúžkuj), ale 6 nie je. Rozlož 6 na 2 × 3. Obe sú prvočísla - zakrúžkuj ich.
💡 Pamätaj si: Vždy sa snaž deliť najmenšími prvočíslami - začni s 2, potom 3, 5, 7...
Praktické príklady rozkladu
Pozrime si číslo 60 - väčšie číslo, ale princíp je rovnaký! Rozlož ho na 6 × 10. Ani jedno nie je prvočíslo, takže pokračuj.
6 = 2 × 3 (obe prvočísla), 10 = 2 × 5 (obe prvočísla). Výsledok: 60 = 2 × 2 × 3 × 5. Môžeš to napísať aj ako 2² × 3 × 5.
Pre číslo 48: Delíme postupne dvojkou - 48 = 2 × 24, potom 24 = 2 × 12, ďalej 12 = 2 × 6, nakoniec 6 = 2 × 3. Dostávame 48 = 2 × 2 × 2 × 2 × 3.
Každé číslo má svoj jedinečný prvočíselný rozklad - je to ako jeho DNA! Bez ohľadu na to, ako začneš rozkladať, vždy dostaneš tie isté prvočísla.
💡 Super tip: Ak si neistý, over si výsledok vynásobením - všetky prvočísla spolu musia dať pôvodné číslo!
Pokročilé techniky a triky
Keď pracuješ s väčšími číslami, pravidlá deliteľnosti sú tvoji najlepší priatelia. Pre číslo 3: zrátal súčet všetkých cifier. Ak je deliteľný 3, aj celé číslo je.
Pre rozklad väčších čísel sa vždy drž stratégie "od najmenšieho k najväčšiemu". Najprv skús všetky dvojky vydeliť, potom trojky, potom päťky a tak ďalej.
Časté chyby: Nezabudni, že číslo 1 nie je prvočíslo! Tiež si daj pozor na číslo 9 - nie je prvočíslo, lebo 9 = 3 × 3.
💡 Profi tip: Ak si pamätáš prvých pár prvočísel (2, 3, 5, 7, 11, 13, 17, 19), rozkladanie bude oveľa rýchlejšie!
Zhrnutie na test
Teraz už máš všetko potrebné na úspech! Prvočíslo má presne 2 delitele (1 a seba), zložené číslo má viac ako 2 delitele.
Pre rozklad na súčin prvočísel použi strom rozkladu - rozkladaj, kým nedostaneš len prvočísla, potom ich všetky vynásob.
Rýchla kontrola: 7 je prvočíslo (delitele: 1, 7), 12 je zložené (delitele: 1, 2, 3, 4, 6, 12), a 12 = 2 × 2 × 3.
💡 Na záver: Táto téma sa ti bude hodiť celý život v matematike - od zlomkov až po pokročilé rovnice. Zvládneš to!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content in Matematika
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Prvočísla a Zložené Čísla: Jednoduché Vysvetlenie
Prvočísla a zložené čísla sú ako stavebné kamene matematiky! Každé prirodzené číslo patrí do jednej z týchto skupín (okrem čísla 1, ktoré je špeciálne). Naučíš sa rozoznať tieto čísla a dokonca aj rozložiť akékoľvek číslo na jeho základné súčasti.
Prvočísla a zložené čísla - základy
Matematika je vlastne ako stavebnica - a prvočísla sú jej najmenšie kocky! Sú to čísla, ktoré majú presne dva delitele: číslo 1 a samo seba. Napríklad 7 sa dá vydeliť len číslom 1 a 7.
Zložené čísla sú väčšie stavby z týchto kociek. Majú viac ako dva delitele. Číslo 6 napríklad môžeš vydeliť číslami 1, 2, 3 a 6 - to sú štyri delitele!
Číslo 1 je úplne špeciálne - nie je ani prvočíslo, ani zložené číslo. Má totiž len jeden deliteľ (seba samého), takže sa do žiadnej skupiny nehodí.
💡 Tip: Číslo 2 je jediné párne prvočíslo! Všetky ostatné párne čísla sú zložené, lebo sa dajú vydeliť aspoň číslom 2.
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Ako rozoznáš prvočíslo od zlženého čísla
Zistiť typ čísla je ako detektívka - musíš nájsť všetkých jeho deliteľov! Začni vždy s číslom 1 a samotným číslom. Potom skúšaj menšie čísla ako 2, 3, 4, 5...
Pravidlá deliteľnosti ti ušetria veľa času. Ak je číslo párne, je deliteľné 2. Ak súčet jeho cifier je deliteľný 3, aj celé číslo je deliteľné 3. Končí na 0 alebo 5? Je deliteľné 5.
Príklad s číslom 17: Nie je párne, súčet cifier je 8 (nie deliteľný 3), nekončí na 0 ani 5. Skús ešte 7 - nevyjde ti to. Máš len deliteľov 1 a 17 = prvočíslo!
💡 Skvelá správa: Nemusíš skúšať všetky čísla! Stačí ísť len do odmocniny z daného čísla, ale zatiaľ sa sústredíme na menšie čísla.
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Rozklad na súčin prvočísel - strom rozkladu
Tu prichádza to najzaujímavejšie! Každé zložené číslo sa dá rozložiť na súčin len prvočísel. Je to ako rozobratá stavebnica na základné kocky.
Strom rozkladu funguje takto: Začni s číslom, ktoré chceš rozložiť. Nájdi dva jeho delitele (okrem 1) a napíš ich pod neho. Spoj ich čiarkami.
Pre číslo 12: Začni s 12, rozlož na 2 × 6. Číslo 2 je prvočíslo (zakrúžkuj), ale 6 nie je. Rozlož 6 na 2 × 3. Obe sú prvočísla - zakrúžkuj ich.
💡 Pamätaj si: Vždy sa snaž deliť najmenšími prvočíslami - začni s 2, potom 3, 5, 7...
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Praktické príklady rozkladu
Pozrime si číslo 60 - väčšie číslo, ale princíp je rovnaký! Rozlož ho na 6 × 10. Ani jedno nie je prvočíslo, takže pokračuj.
6 = 2 × 3 (obe prvočísla), 10 = 2 × 5 (obe prvočísla). Výsledok: 60 = 2 × 2 × 3 × 5. Môžeš to napísať aj ako 2² × 3 × 5.
Pre číslo 48: Delíme postupne dvojkou - 48 = 2 × 24, potom 24 = 2 × 12, ďalej 12 = 2 × 6, nakoniec 6 = 2 × 3. Dostávame 48 = 2 × 2 × 2 × 2 × 3.
Každé číslo má svoj jedinečný prvočíselný rozklad - je to ako jeho DNA! Bez ohľadu na to, ako začneš rozkladať, vždy dostaneš tie isté prvočísla.
💡 Super tip: Ak si neistý, over si výsledok vynásobením - všetky prvočísla spolu musia dať pôvodné číslo!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Pokročilé techniky a triky
Keď pracuješ s väčšími číslami, pravidlá deliteľnosti sú tvoji najlepší priatelia. Pre číslo 3: zrátal súčet všetkých cifier. Ak je deliteľný 3, aj celé číslo je.
Pre rozklad väčších čísel sa vždy drž stratégie "od najmenšieho k najväčšiemu". Najprv skús všetky dvojky vydeliť, potom trojky, potom päťky a tak ďalej.
Časté chyby: Nezabudni, že číslo 1 nie je prvočíslo! Tiež si daj pozor na číslo 9 - nie je prvočíslo, lebo 9 = 3 × 3.
💡 Profi tip: Ak si pamätáš prvých pár prvočísel (2, 3, 5, 7, 11, 13, 17, 19), rozkladanie bude oveľa rýchlejšie!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Zhrnutie na test
Teraz už máš všetko potrebné na úspech! Prvočíslo má presne 2 delitele (1 a seba), zložené číslo má viac ako 2 delitele.
Pre rozklad na súčin prvočísel použi strom rozkladu - rozkladaj, kým nedostaneš len prvočísla, potom ich všetky vynásob.
Rýchla kontrola: 7 je prvočíslo (delitele: 1, 7), 12 je zložené (delitele: 1, 2, 3, 4, 6, 12), a 12 = 2 × 2 × 3.
💡 Na záver: Táto téma sa ti bude hodiť celý život v matematike - od zlomkov až po pokročilé rovnice. Zvládneš to!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user