Q: What are the prime factors of the number 219,564?

 A: 2, 3, 19, 107

Why are those the prime factors of the number 219,564?

Prime factors are the prime numbers that can be multipled together to equal the original number. You find the factors by dividing by prime numbers. It is best shown by creating a Factor Tree.

Factor Tree for the number 219,564

219,564
Factor Arrows
2109,782
Factor Arrows
254,891
Factor Arrows
318,297
Factor Arrows
36,099
Factor Arrows
32,033
Factor Arrows
19107

The numbers in bold above are the prime factors. If there are multiples, you only count them one time. This leads us to our prime factors of:

2, 3, 19, 107

We can check our work by multiplying all of the prime factors together: 2 x 2 x 3 x 3 x 3 x 19 x 107 = 219,564

This can also be written as 22 x 33 x 191 x 1071 = 219,564

If you would like to know more, or need additional explanation, please review our prime factorization explanation.


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