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HCF and LCM, Law of Indices, Standard Form, and Surds: Examples, Questions, and Worksheets

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An Pham

1/16/2023

Maths

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HCF and LCM, Law of Indices, Standard Form, and Surds: Examples, Questions, and Worksheets

The highest common factor (HCF) and lowest common multiple (LCM) are fundamental mathematical concepts, alongside laws of indices, standard form, and surds. These concepts form essential building blocks for advanced mathematics and problem-solving.

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1/16/2023

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HCF and LCM, Law of Indices, Standard Form, and Surds: Examples, Questions, and Worksheets

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An Pham

@apham

The highest common factor (HCF) and lowest common multiple (LCM) are fundamental mathematical concepts, alongside laws of indices, standard form, and surds. These concepts form essential building blocks for advanced mathematics and problem-solving.


<p>HCF stands for Highest Common Factor, which is the largest number that divides exactly into 2 or more numbers. An example of this is the

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Page 1: Mathematical Foundations: HCF, LCM, Indices, Standard Form, and Surds

This comprehensive page covers several key mathematical concepts essential for GCSE mathematics. The content begins with hcf and lcm examples and extends to cover indices, standard form, and surds.

Starting with HCF and LCM calculations, the page demonstrates how to use prime factorization to find these values. The law of indices formula section follows, explaining various rules for working with powers. Finally, it covers standard form notation and introduces the concept of surds.

Definition: HCF (Highest Common Factor) is the largest number that divides exactly into two or more numbers.

Example: The HCF of 12 and 20 is 4, as demonstrated through prime factorization.

Definition: LCM (Lowest Common Multiple) is the smallest number that appears in the times tables of two or more numbers.

Example: Using hcf and lcm calculator principles, the LCM of 12 and 20 is 60.

Highlight: When working with indices, remember that multiplying terms with the same base requires adding the powers, while division requires subtracting them.

Vocabulary: A surd is an irrational number that can be written exactly using square or cube roots.

Key sections covered:

  1. HCF and LCM calculations using prime factorization
  • Example working through 24 and 60
  • Use of factor trees for prime factorization
  • Hcf and lcm questions and answers demonstrated
  1. Laws of Indices
  • Addition of powers when multiplying
  • Subtraction of powers when dividing
  • Rules for zero and negative indices
  • Fractional indices and roots
  1. Standard Form
  • Writing numbers in the form A × 10ⁿ
  • Converting between standard and ordinary form
  • Applications for very large and small numbers
  1. Surds
  • Definition and identification
  • Basic operations with surds
  • Simplification rules
  • Examples of surd calculations

The page provides comprehensive coverage of these topics with clear examples and explanations, making it an excellent resource for GCSE mathematics revision.

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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

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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

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Greenlight Bonnie

Android user

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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