Year 7 - Maths
Highest common factor
Properties of number: factors, multiples, squares and cubes
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils develop their understanding of factors and multiples, then extend this knowledge to learn general divisibility tests for integers and develop strategies to determine the highest common factor and lowest common multiple of two or more integers.
Lesson Summary
You will learn to use the prime factorisation of two or more positive integers to efficiently identify the highest common factor.
Key Notes
- Common factors can be found by comparing the products of their primes.
- The highest common factor of two numbers can be found by comparing the prime factorisation of both numbers.
- Sometimes a Venn diagram can help identify the highest common factor of two numbers.
- The highest common factor of more than two numbers can be found using prime factorisation.
Vocabulary To Learn
- Prime factorisation: a method to find the prime factors of a given integer
- Highest common factor: The highest common factor of two or more integers which can be divided by all other possible common factors
- HCF: an abbreviation for highest common factor
Common Mistakes To Avoid
- Common factors are put into the intersection of the Venn diagram twice instead of once.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Common factors can be found by comparing the products of their primes. The highest common factor of two numbers can be found by comparing the prime factorisation of both numbers.
2. Use this key word in a maths sentence and explain it clearly. 'Prime factorisation'
a method to find the prime factors of a given integer. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Common factors are put into the intersection of the Venn diagram twice instead of once. Correction: Encourage students to check that the product of the factors in each set is the correct integer.
More Lessons In This Unit
- Calculating integers from their prime factor expressions Study Guide
- Checking understanding of factors, multiples, squares and cubes Study Guide
- Checking understanding of prime numbers Study Guide
- Divisibility tests for 2 and 3 Study Guide
- Divisibility tests for 4 and 8 Study Guide
- Divisibility tests for 5 and 10 Study Guide
- Divisibility tests for 6 and 9 Study Guide
- Expressing an integer as a product of its prime factors Study Guide
- HCF or LCM Study Guide
- Listing factors Study Guide
- Listing multiples Study Guide
- Lowest common multiple Study Guide
- Power notation Study Guide
- Powers and roots using a calculator Study Guide
- Problem solving with factors, multiples, squares and cubes Study Guide
- Securing understanding of factors, multiples, squares and cubes Study Guide
- Square and cube numbers Study Guide
- Square and cube roots Study Guide
Browse all guides in the Year 7 Maths guide library.