# How do you identify all of the prime factors of a number?

All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.

Example: 210

210 Divide by two.

105,2 Divide by three.

35,3,2 Divide by five.

7,5,3,2 Stop. All the factors are prime.

2 x 3 x 5 x 7 = 210

That's the prime factorization of 210.

### Would you rather find all the factors of a number or find all the prime factors of a number?

Once all the prime factors of a number have been found, the number of factors the number has and what they are can be found. I'd be finding the prime factors first before finding all the factors of a number, so I'd rather find all the prime factors as it means I can stop before I have to do more work in finding all the factors.

### What is a prime factor of twelve?

To find the prime factors all you need to do is find all factors, and identify which ones are prime numbers. 12=1*12=2*6=3*4 factors=1,2,3,4,6,12 Prime numbers can only be divided by 1 and the number itself. Thus the prime factors of 12 are 2 and 3 (1 is, by definition, not prime (i'm not exactly sure how to explain why))