Year 7 - Maths
Calculating integers from their prime factor expressions
Properties of number: factors, multiples, squares and cubes
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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 evaluate a number written as a product of its prime factors.
Key Notes
- Evaluating a product of primes will give a unique positive integer.
- It is useful to compare numbers using their prime factor product without evaluating the numbers.
- Square numbers can be identified from their product of primes.
- Common factors can be found by comparing the products of their primes.
Vocabulary To Learn
- Composite number: A composite number is an integer with more than two factors.
- Product: A product is the result of two or more numbers multiplied together.
- Prime factors: Prime factors are factors of a number that are, themselves, prime.
- Exponent: An exponent is a number positioned above and to the right of a base value. It indicates repeated multiplication.
Common Mistakes To Avoid
- Identifying if integer is a multiple when its given in its prime factor form.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Evaluating a product of primes will give a unique positive integer. It is useful to compare numbers using their prime factor product without evaluating the numbers.
2. Use this key word in a maths sentence and explain it clearly. 'Composite number'
A composite number is an integer with more than two factors. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Identifying if integer is a multiple when its given in its prime factor form. Correction: Only the bases need to be considered, not the exponents. e.g if it is a multiple of 3 it must be a multiple of 3^2, 3^3, etc.
More Lessons In This Unit
- 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 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.