Year 8: Prime factor decomposition

Prime factor decomposition is finding the prime numbers that multiply together to equal a given number. Let’s break it down!

What are Prime Numbers?

A prime number is a whole number greater than 1 that has only two divisors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13, etc.

How to do it

1. Start with the number you want to decompose. Let's say we want to decompose 36.
2. Find the smallest prime number that divides evenly into the number. The smallest prime number that divides 36 is 2. (36 / 2 = 18)
3. Divide the number by that prime number. 36 / 2 = 18
4. Repeat this process with the new number. 18 is divisible by 2. (18 / 2 = 9)
5. Continue dividing by prime numbers until you are left with only prime numbers. 9 is not divisible by 2. The next prime number is 3. (9 / 3 = 3)
6. You'll end up with a product of prime numbers. So, the prime factor decomposition of 36 is 2 x 2 x 3 x 3, or 2² x 3².

Example: Decomposing 48

1. 48 / 2 = 24
2. 24 / 2 = 12
3. 12 / 2 = 6
4. 6 / 2 = 3
5. 3 / 3 = 1

Result: 2 x 2 x 2 x 2 x 3 = 2⁴ x 3

Practice is key: Try decomposing different numbers.