How do you find prime factors?

Answer 1

To determine the prime factors of a number:

Try to divide the number by the lowest Prime number, which is 2. If it divides evenly mark that number down as one of the prime factors, and continue with the result, trying to divide that prime factor into it. Continue dividing that prime factor into the results until it no longer divides evenly. If it does not divide evenly, move to the next lowest prime number and repeat the process until you have a result that is a prime number. Now you have all the prime factors.

Example: Find the prime factors of 128.

The prime factors are in bold.

128 ÷ 2 = 64

64 ÷ 2 = 32

32 ÷ 2 = 16

16 ÷ 2 = 8

8 ÷ 2 = 4

4 ÷ 2 = 2 which is a prime factor and thus the final prime factor.

Therefore, the prime factors of 128 are 2, 2, 2, 2, 2, 2, and 2; the prime factorization is 2 x 2 x 2 x 2 x 2 x 2 x 2.

Example: Find the prime factors of 108.

108 ÷ 2 = 54

54 ÷ 2 = 27

27 is not divisible by 2, so try 3.

27 ÷ 3 = 9

9 ÷ 3 = 3 which is a prime factor and thus the final prime factor.

Therefore the prime factors of 108 are 2, 2, 3, 3, and 3; the prime factorization is 2 x 2 x 3 x 3 x 3.

Example: Find the prime factors of 1463.

1463 is not divisible by 2 or 3 or 5, but it is divisible by 7.

1463 ÷ 7 = 209

209 is not divisible 7, so try the next prime number, which is 11.

209 ÷ 11 = 19 which is a prime factor and thus the final prime factor.

Therefore, the prime factors of 1463 are 7, 11, and 19; the prime factorization is 7 x 11 x 19.

Another way to determine the prime factors is to use a factor tree. To make a factor tree, find two numbers whose product is the given number. Then, if those numbers are not prime, do the same for them. Continue until all numbers are prime.

Example: Find the prime factors of 54 using a factor tree.

54

6 x 9

2x3 x 3x3

Therefore, the prime factors of 54 are 2, 3, 3, and 3; the prime factorization is 2 x 3 x 3 x 3.

For other examples of factor trees, see the related question on factoring terminology.
you find it by using exponents and by dividing the two numbers
you do a mutiple of that to get the number you re factoring by then make prime factor tree

Answer 2

A prime number is a whole number greater than 1, whose only two whole-number factors are 1 and itself.