Prime factorization

Here is an example

What are the prime factors of 12 ? It is best to start working from the smallest prime number, which is 2, so let's check: 12 ÷ 2 = 6 Yes, it divided evenly by 2. We have taken the first step! But 6 is not a prime number, so we need to go further. Let's try 2 again: 6 ÷ 2 = 3 Yes, that worked also. And 3 is a prime number, so we have the answer: 12 = 2 × 2 × 3 As you can see, every factor is a prime number, so the answer must be right. Note: 12 = 2 × 2 × 3 can also be written using exponents as 12 = 2squared × 3

What if you start with a large number?

What are the prime factors of 90 ? Break 90 into 9 × 10 The prime factors of 9 are 3 and 3 The prime factors of 10 are 2 and 5 So the prime factors of 90 are 3, 3, 2 and 5

Here is another example

What is the prime factorization of 147 ? Can we divide 147 evenly by 2? No, so we should try the next prime number, 3: 147 ÷ 3 = 49 Then we try factoring 49, and find that 7 is the smallest prime number that works: 49 ÷ 7 = 7 And that is as far as we need to go, because all the factors are prime numbers. 147 = 3 × 7 × 7 (or 147 = 3 × 7squared using exponents)

And another

What is the prime factorization of 17 ? Hang on ... 17 is a Prime Number. So that is as far as we can go. 17 = 17

What is prime factorization

"Prime Factorization" is finding which prime numbers multiply together to make the original number.