Year 7 - Maths
Expressing an integer as a product of its prime factors
Properties of number: factors, multiples, squares and cubes
Study Hub
Study Guides
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 write any positive integer uniquely as a product of its prime factors.
Key Notes
- Every composite number has prime number factors.
- All the factors of a number can be broken down into prime factors.
- Every positive integer can be broken down into prime factors.
- Every positive integer can be written as a product of its prime factors.
- Prime factor products can be simplified by using index notation.
Vocabulary To Learn
- Composite: A composite number is an integer with more than two factors. All integers greater than 1 are either composite or prime
- Prime factors: Prime factors are the factors of a number that are, themselves, prime.
- Unique: Each composite number has a unique product of its prime factors. i.e. there is only one unique way it can be written.
Common Mistakes To Avoid
- Use of addition instead of multiplication when the decomposing the number.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Every composite number has prime number factors. All the factors of a number can be broken down into prime factors.
2. Use this key word in a maths sentence and explain it clearly. 'Composite'
A composite number is an integer with more than two factors. All integers greater than 1 are either composite or prime. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Use of addition instead of multiplication when the decomposing the number. Correction: Reiterate that the product of prime factors is unique.
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
- 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.