Year 7 - Maths
Listing factors
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 state what a factor is and can identify factors of positive integers.
Key Notes
- Divisibility tests can help identify factors of a number.
- Using factors pairs it is possible to systematically find all the factors of an integer.
- It is possible to identify common factors by finding all the factors of 2 or more numbers and comparing them.
- It is possible to identify common factors of large numbers by listing all the factors but this is time consuming.
- To simplify fractions it may be helpful to identify the highest common factor.
Vocabulary To Learn
- Numerical factor: A numerical factor is a factor that is an integer.
- Product: A product is the result of two or more numbers multiplied together.
- Divisibility: Divisibility is a number's ability to be exactly divided by another number, leaving no remainder.
Common Mistakes To Avoid
- Students often use an adhoc approach to listing multiples this often leads to pairs being missed out
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Divisibility tests can help identify factors of a number. Using factors pairs it is possible to systematically find all the factors of an integer.
2. Use this key word in a maths sentence and explain it clearly. 'Numerical factor'
A numerical factor is a factor that is an integer. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Students often use an adhoc approach to listing multiples this often leads to pairs being missed out. Correction: Encourage a systematic approach starting with 1 and the 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
- Highest common factor 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.