Year 9: Prime factor decomposition

This cheat sheet helps you break down numbers into their prime factors.

What are Prime Factors?

Prime factors are prime numbers that, when multiplied together, result in the original number. A prime number is a whole number greater than 1 that has only two divisors: 1 and itself (e.g., 2, 3, 5, 7, 11).

Steps for Prime Factor Decomposition

1. Divide by the smallest prime number that divides evenly: Start with 2. If the number is even, divide it by 2 until it's no longer divisible by 2.
2. Repeat with the next prime number: After dividing by 2, move to the next prime number, which is 3. Continue dividing by 3 as long as it divides evenly.
3. Continue until you have only prime factors left: Keep repeating this process with the next prime number (5, 7, 11, etc.) until the remaining number is 1.

Example: Decomposing 36

1. 36 is divisible by 2: 36 / 2 = 18
2. 18 is divisible by 2: 18 / 2 = 9
3. 9 is divisible by 3: 9 / 3 = 3
4. 3 is a prime number, so we stop.

Therefore, the prime factorization of 36 is 2 x 2 x 3 x 3, or 2² x 3²

Key Reminders

• Always start with the smallest prime number (2).
• Only use prime numbers as factors.
• Keep dividing until you reach 1.

Good luck!