Year 7 · Maths · Primes, factors and probability · Lesson 2
HCF, LCM and prime factors
Find the highest common factor and lowest common multiple of two numbers, write numbers as products of prime factors, and solve problems.
24-minute video lesson
Teaching, worked examples and 20 practice questions solved step by step.
Watch free for a monthWhat your child will learn
- Find the HCF of two numbers
- Find the LCM of two numbers
- Write a number as a product of primes
- Use prime factors to find the HCF
- Solve HCF and LCM problems
The method
- HCF: list factors, find the biggest in both.
- LCM: list multiples, find the first in both.
- Prime factors: keep dividing by primes.
- Groups: HCF. Repeating events: LCM.
Key words: HCF, LCM, prime factor, common factor, common multiple.
Worked examples
The first three practice questions from the lesson, with every step.
Question 1
Find the highest common factor (HCF) of 8 and 12.
- Step 1: Factors of 8: 1, 2, 4, 8
- Step 2: Factors of 12: 1, 2, 3, 4, 6, 12
- Step 3: Common: 1, 2, 4. Highest: 4
Answer: 4
Question 2
Find the highest common factor (HCF) of 15 and 25.
- Step 1: Factors of 15: 1, 3, 5, 15
- Step 2: Factors of 25: 1, 5, 25
- Step 3: Common: 1, 5. Highest: 5
Answer: 5
Question 3
Find the highest common factor (HCF) of 18 and 30.
- Step 1: Factors of 18: 1, 2, 3, 6, 9, 18
- Step 2: Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Step 3: Common: 1, 2, 3, 6. Highest: 6
Answer: 6