Year 7 - Maths
Divisibility tests for 4 and 8
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 identify and explain whether a number is or is not a multiple of a given integer.
Key Notes
- A number is a multiple of 4 if and only if the last two digits are a multiple of 4.
- Any multiple of 4 is also a multiple of 2.
- A number is a multiple of 8 if and only if the last three digits are a multiple of 8.
- Any multiple of 8 is also a multiple of 4 and 2.
Vocabulary To Learn
- Divisibility: Divisibility is a number's ability to be exactly divided by another number, leaving no remainder.
Common Mistakes To Avoid
- Often students only consider the last 2 digits of a number to check for divisibility for 8.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A number is a multiple of 4 if and only if the last two digits are a multiple of 4. Any multiple of 4 is also a multiple of 2.
2. Use this key word in a maths sentence and explain it clearly. 'Divisibility'
Divisibility is a number's ability to be exactly divided by another number, leaving no remainder. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Often students only consider the last 2 digits of a number to check for divisibility for 8. Correction: The last 2 digits check for divisibility for 4 not 8.
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 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 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.