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How to Find the Biggest Prime Factor and Learn Divisibility Rules for 7th Grade Math

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How to Find the Biggest Prime Factor and Learn Divisibility Rules for 7th Grade Math
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Shaivi Ramisetti

@shaivi711

·

73 Followers

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A comprehensive guide to prime numbers, divisibility rules, and ratio calculations in mathematics. This guide covers essential mathematical concepts including cómo encontrar el factor primo más grande de un conjunto de números, reglas de divisibilidad para matemáticas de séptimo grado, and cómo calcular el mínimo común múltiplo y el máximo común divisor.

Key concepts covered:

  • Prime and composite numbers identification
  • Divisibility rules for numbers 2 through 10
  • Greatest Common Factor (GCF) calculation methods
  • Least Common Multiple (LCM) determination
  • Ratio and rate calculations
  • Unit rates and pricing applications

5/10/2023

130

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

View

Ratio Tables

This page introduces the concept of ratio tables, which are useful tools for visualizing and calculating equivalent ratios.

Definition: A ratio table is a table with columns filled with pairs of numbers representing equivalent ratios.

The page outlines two main methods for creating ratio tables:

  1. Finding equivalent ratios
  2. Scaling ratios up or down

Ratio tables are particularly useful for:

  • Organizing information about proportional relationships
  • Finding missing values in proportional situations
  • Comparing ratios and rates

Understanding how to create and use ratio tables is essential for solving problems involving proportions, scaling, and unit conversions.

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

View

Rates

This page introduces the concept of rates, unit rates, and unit prices, which are essential for comparing quantities measured in different units.

Definition: A rate is a comparison of quantities measured in different units.

Definition: A unit rate is a rate that is simplified to have a denominator of 1.

Definition: A unit price is the cost per unit of a product.

The page provides examples and methods for calculating unit rates and unit prices:

Example: Manuel reads 1,000 words in 5 minutes. The unit rate is 200 words per minute.

Example: Imena earned $225 for 18 hours of work. Her unit rate (hourly wage) is $12.50 per hour.

The page also demonstrates how to use unit rates to solve more complex problems, such as comparing heart rates of different animals over time.

Understanding rates and unit rates is crucial for solving problems involving speed, pricing, and other real-world applications.

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

View

Ratios

This page introduces the concept of ratios, which is fundamental for comparing quantities in various mathematical and real-world contexts.

Definition: A ratio is a comparison of two quantities by division.

The page explains that ratios can be expressed in three forms:

  1. Using a colon (e.g., 3:4)
  2. Using the word "to" (e.g., 3 to 4)
  3. As a fraction (e.g., 3/4)

Example: In a basket with 6 apples, 4 bananas, and 3 oranges:

  • Ratio of bananas to apples: 4:6, 4 to 6, or 4/6 (simplified to 2:3)
  • Ratio of bananas and apples to oranges: 10:3, 10 to 3, or 10/3
  • Ratio of oranges to total fruit: 3:13, 3 to 13, or 3/13

The page emphasizes the importance of simplifying ratios to their lowest terms and using ratios to compare categorical data.

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

View

Factors and Multiples

This page introduces the concepts of greatest common factor (GCF) and least common multiple (LCM), which are fundamental for cómo calcular el mínimo común múltiplo y el máximo común divisor.

Definition: The Greatest Common Factor (GCF) is the largest factor shared by a set of numbers.

Definition: A multiple is the product of a number and a non-zero whole number.

The page outlines methods for finding the GCF and LCM:

  1. For GCF: Use factor trees to find prime factors, circle common factors, and multiply them.
  2. For LCM: Create factor trees, select equal amounts of common prime factors, and multiply all prime factors plus leftovers.

Highlight: The GCF cannot be larger than the smallest number in the set.

Highlight: The LCM cannot be smaller than the largest number in the set.

These concepts are crucial for simplifying fractions, solving equations, and understanding number relationships.

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

View

Least Common Multiple

This page delves deeper into the concept of least common multiple (LCM), which is essential for cómo calcular el mínimo común múltiplo y el máximo común divisor.

Definition: The Least Common Multiple (LCM) of two or more numbers is the smallest number that is a multiple of all the given numbers.

The page provides a step-by-step method for finding the LCM:

  1. Create prime factor trees for each number.
  2. Select equal amounts of common prime factors from each tree.
  3. Look for common prime factors left or common pairs.
  4. Multiply all prime factors plus leftovers.

Example: To find the LCM of 32 and 78: 32 = 2 x 2 x 2 x 2 x 2 78 = 2 x 3 x 13 LCM = 2 x 2 x 2 x 2 x 2 x 3 x 13 = 624

Understanding LCM is crucial for solving problems involving fractions, time intervals, and periodic events.

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

View

More Rate Problems

This page provides additional examples and problem-solving techniques for working with rates and unit rates.

The page includes a complex example comparing cat and horse heart rates:

Example: A cat's heart beats 3,600 times in 30 minutes, while a horse's heart beats 1,320 times in 30 minutes. To find how many more times a cat's heart beats in 60 minutes:

  1. Calculate unit rates: Cat = 120 beats/min, Horse = 44 beats/min
  2. Multiply by 60 minutes: Cat = 7,200 beats, Horse = 2,640 beats
  3. Find the difference: 7,200 - 2,640 = 4,560 beats

The page also includes a simpler example of calculating unit price:

Example: Heather spent $96 on four concert tickets. The unit price (price per ticket) is $24.

These examples demonstrate the versatility of rate calculations in solving various types of problems.

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

View

Prime and Composite Numbers

This page introduces the fundamental concepts of prime and composite numbers, which are crucial for understanding factors and multiples.

Definition: A prime number is a number that has only two factors: 1 and itself.

Definition: A composite number is a number that has three or more factors.

The page includes a hundred chart highlighting prime numbers up to 100, providing a visual representation of the distribution of prime numbers.

Example: Prime numbers include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, etc.

Example: Composite numbers include 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, etc.

Understanding the difference between prime and composite numbers is essential for cómo encontrar el factor primo más grande de un conjunto de números and other mathematical operations.

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

View

Divisibility Rules

This page outlines the divisibility rules for numbers 2 through 10, which are essential reglas de divisibilidad para matemáticas de séptimo grado.

Definition: Divisibility rules are shortcuts to determine if a number is divisible by another without performing the division.

The page provides detailed explanations for each divisibility rule:

  1. Divisible by 2: If the last digit is even.
  2. Divisible by 3: If the sum of the digits is divisible by 3.
  3. Divisible by 4: If the last two digits form a number divisible by 4.
  4. Divisible by 5: If the last digit is 0 or 5.
  5. Divisible by 6: If the number is divisible by both 2 and 3.

Example: 810 is divisible by 3 because 8 + 1 + 0 = 9, and 9 is divisible by 3.

Example: 916 is divisible by 4 because 16 is divisible by 4.

These rules are crucial for simplifying calculations and understanding number properties.

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

View

More Divisibility Rules

This page continues with the divisibility rules for numbers 7 through 10, completing the set of reglas de divisibilidad para matemáticas de séptimo grado.

  1. Divisible by 7: Double the last digit and subtract it from the rest of the number. If the result is divisible by 7, the original number is divisible by 7.
  2. Divisible by 8: If the last three digits form a number divisible by 8.
  3. Divisible by 9: If the sum of all digits is divisible by 9.
  4. Divisible by 10: If the number ends in 0.

Example: For 112 to be divisible by 7: Double the last digit (2 x 2 = 4), subtract from the rest (11 - 4 = 7). Since 7 is divisible by 7, 112 is divisible by 7.

Example: 4,168 is divisible by 8 because 168 is divisible by 8.

These rules are valuable tools for mental math and problem-solving in various mathematical contexts.

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

View

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Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

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Download in

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Knowunity is the # 1 ranked education app in five European countries

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Students use Knowunity

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I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

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The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

Subjects

/

Arithmetic

/

Proportions

/

Writing & solving proportions

/

Multi-step ratio and percent problems

How to Find the Biggest Prime Factor and Learn Divisibility Rules for 7th Grade Math

user profile picture

Shaivi Ramisetti

@shaivi711

·

73 Followers

Follow

A comprehensive guide to prime numbers, divisibility rules, and ratio calculations in mathematics. This guide covers essential mathematical concepts including cómo encontrar el factor primo más grande de un conjunto de números, reglas de divisibilidad para matemáticas de séptimo grado, and cómo calcular el mínimo común múltiplo y el máximo común divisor.

Key concepts covered:

  • Prime and composite numbers identification
  • Divisibility rules for numbers 2 through 10
  • Greatest Common Factor (GCF) calculation methods
  • Least Common Multiple (LCM) determination
  • Ratio and rate calculations
  • Unit rates and pricing applications

5/10/2023

130

 

7th

 

Arithmetic

6

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

Ratio Tables

This page introduces the concept of ratio tables, which are useful tools for visualizing and calculating equivalent ratios.

Definition: A ratio table is a table with columns filled with pairs of numbers representing equivalent ratios.

The page outlines two main methods for creating ratio tables:

  1. Finding equivalent ratios
  2. Scaling ratios up or down

Ratio tables are particularly useful for:

  • Organizing information about proportional relationships
  • Finding missing values in proportional situations
  • Comparing ratios and rates

Understanding how to create and use ratio tables is essential for solving problems involving proportions, scaling, and unit conversions.

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

Rates

This page introduces the concept of rates, unit rates, and unit prices, which are essential for comparing quantities measured in different units.

Definition: A rate is a comparison of quantities measured in different units.

Definition: A unit rate is a rate that is simplified to have a denominator of 1.

Definition: A unit price is the cost per unit of a product.

The page provides examples and methods for calculating unit rates and unit prices:

Example: Manuel reads 1,000 words in 5 minutes. The unit rate is 200 words per minute.

Example: Imena earned $225 for 18 hours of work. Her unit rate (hourly wage) is $12.50 per hour.

The page also demonstrates how to use unit rates to solve more complex problems, such as comparing heart rates of different animals over time.

Understanding rates and unit rates is crucial for solving problems involving speed, pricing, and other real-world applications.

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

Ratios

This page introduces the concept of ratios, which is fundamental for comparing quantities in various mathematical and real-world contexts.

Definition: A ratio is a comparison of two quantities by division.

The page explains that ratios can be expressed in three forms:

  1. Using a colon (e.g., 3:4)
  2. Using the word "to" (e.g., 3 to 4)
  3. As a fraction (e.g., 3/4)

Example: In a basket with 6 apples, 4 bananas, and 3 oranges:

  • Ratio of bananas to apples: 4:6, 4 to 6, or 4/6 (simplified to 2:3)
  • Ratio of bananas and apples to oranges: 10:3, 10 to 3, or 10/3
  • Ratio of oranges to total fruit: 3:13, 3 to 13, or 3/13

The page emphasizes the importance of simplifying ratios to their lowest terms and using ratios to compare categorical data.

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

Factors and Multiples

This page introduces the concepts of greatest common factor (GCF) and least common multiple (LCM), which are fundamental for cómo calcular el mínimo común múltiplo y el máximo común divisor.

Definition: The Greatest Common Factor (GCF) is the largest factor shared by a set of numbers.

Definition: A multiple is the product of a number and a non-zero whole number.

The page outlines methods for finding the GCF and LCM:

  1. For GCF: Use factor trees to find prime factors, circle common factors, and multiply them.
  2. For LCM: Create factor trees, select equal amounts of common prime factors, and multiply all prime factors plus leftovers.

Highlight: The GCF cannot be larger than the smallest number in the set.

Highlight: The LCM cannot be smaller than the largest number in the set.

These concepts are crucial for simplifying fractions, solving equations, and understanding number relationships.

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

Least Common Multiple

This page delves deeper into the concept of least common multiple (LCM), which is essential for cómo calcular el mínimo común múltiplo y el máximo común divisor.

Definition: The Least Common Multiple (LCM) of two or more numbers is the smallest number that is a multiple of all the given numbers.

The page provides a step-by-step method for finding the LCM:

  1. Create prime factor trees for each number.
  2. Select equal amounts of common prime factors from each tree.
  3. Look for common prime factors left or common pairs.
  4. Multiply all prime factors plus leftovers.

Example: To find the LCM of 32 and 78: 32 = 2 x 2 x 2 x 2 x 2 78 = 2 x 3 x 13 LCM = 2 x 2 x 2 x 2 x 2 x 3 x 13 = 624

Understanding LCM is crucial for solving problems involving fractions, time intervals, and periodic events.

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

More Rate Problems

This page provides additional examples and problem-solving techniques for working with rates and unit rates.

The page includes a complex example comparing cat and horse heart rates:

Example: A cat's heart beats 3,600 times in 30 minutes, while a horse's heart beats 1,320 times in 30 minutes. To find how many more times a cat's heart beats in 60 minutes:

  1. Calculate unit rates: Cat = 120 beats/min, Horse = 44 beats/min
  2. Multiply by 60 minutes: Cat = 7,200 beats, Horse = 2,640 beats
  3. Find the difference: 7,200 - 2,640 = 4,560 beats

The page also includes a simpler example of calculating unit price:

Example: Heather spent $96 on four concert tickets. The unit price (price per ticket) is $24.

These examples demonstrate the versatility of rate calculations in solving various types of problems.

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

Prime and Composite Numbers

This page introduces the fundamental concepts of prime and composite numbers, which are crucial for understanding factors and multiples.

Definition: A prime number is a number that has only two factors: 1 and itself.

Definition: A composite number is a number that has three or more factors.

The page includes a hundred chart highlighting prime numbers up to 100, providing a visual representation of the distribution of prime numbers.

Example: Prime numbers include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, etc.

Example: Composite numbers include 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, etc.

Understanding the difference between prime and composite numbers is essential for cómo encontrar el factor primo más grande de un conjunto de números and other mathematical operations.

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

Divisibility Rules

This page outlines the divisibility rules for numbers 2 through 10, which are essential reglas de divisibilidad para matemáticas de séptimo grado.

Definition: Divisibility rules are shortcuts to determine if a number is divisible by another without performing the division.

The page provides detailed explanations for each divisibility rule:

  1. Divisible by 2: If the last digit is even.
  2. Divisible by 3: If the sum of the digits is divisible by 3.
  3. Divisible by 4: If the last two digits form a number divisible by 4.
  4. Divisible by 5: If the last digit is 0 or 5.
  5. Divisible by 6: If the number is divisible by both 2 and 3.

Example: 810 is divisible by 3 because 8 + 1 + 0 = 9, and 9 is divisible by 3.

Example: 916 is divisible by 4 because 16 is divisible by 4.

These rules are crucial for simplifying calculations and understanding number properties.

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

More Divisibility Rules

This page continues with the divisibility rules for numbers 7 through 10, completing the set of reglas de divisibilidad para matemáticas de séptimo grado.

  1. Divisible by 7: Double the last digit and subtract it from the rest of the number. If the result is divisible by 7, the original number is divisible by 7.
  2. Divisible by 8: If the last three digits form a number divisible by 8.
  3. Divisible by 9: If the sum of all digits is divisible by 9.
  4. Divisible by 10: If the number ends in 0.

Example: For 112 to be divisible by 7: Double the last digit (2 x 2 = 4), subtract from the rest (11 - 4 = 7). Since 7 is divisible by 7, 112 is divisible by 7.

Example: 4,168 is divisible by 8 because 168 is divisible by 8.

These rules are valuable tools for mental math and problem-solving in various mathematical contexts.

Le "Prime # = has only 2 factors, itself ex. 3x1 one and Composite # = has 3 or more factors. ex. 12 = 3x4 or bx 2 2 3 * 5 X@XX以 返13 这以以 (17

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Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

13 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying