A factor divides a number exactly, with no remainder.
Example: 3 is a factor of 12 because 12 ÷ 3 = 4.
The factors of 12 are 1, 2, 3, 4, 6 and 12.
2. What is a prime number?
A prime number is a whole number greater than 1 with exactly two positive factors: 1 and itself.
Examples: 2, 3, 5, 7, 11, 13. Remember: 1 is not prime.
3. Prime factorisation
Break a number into a multiplication of prime numbers. Divide by the smallest possible prime each time.
24 = 2 × 12 = 2 × 2 × 6 = 2 × 2 × 2 × 3
In the exercise, type 2x2x2x3. Do not use powers.
4. Highest Common Factor (HCF)
Find the prime factors shared by all numbers and multiply them.
12 = 2 × 2 × 3 18 = 2 × 3 × 3
Shared prime factors: 2 × 3, so HCF = 6.
If there are no shared prime factors, the HCF is 1.
5. Lowest Common Multiple (LCM)
Use each prime factor as many times as needed to make both numbers.
12 = 2 × 2 × 3 18 = 2 × 3 × 3
Take 2 × 2 × 3 × 3, so LCM = 36.
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