How do you find the prime factorization of 34?

Answer 1

One way to find the prime factorization of a number is to start with the lowest Prime number and see if it evenly divides the number. If it does, check whether the result of the division is divisible by that same prime number. When the prime number you are testing does not evenly divide that number, continue with the next prime number. Continue this until the result of the division is a prime number.

Check whether 34 is divisible by 2:
34 ÷ 2 = 17
17 is a prime number, so the prime factorization is finished.
The prime factorization of 34 is 2 x 17.

Another way to find the prime factorization of a number is to choose a factor pair for that number. Then, find a factor pair for each of those numbers that is not prime.

A factor tree of 34 is
34
/ \
2 17

Both 2 and 17 are prime, so the tree is finished.
The prime factorization of 34 is 2 x 17.