Q: What are the prime factors of the number 153,504?

 A: 2, 3, 13, 41

Why are those the prime factors of the number 153,504?

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 153,504

153,504
Factor Arrows
276,752
Factor Arrows
238,376
Factor Arrows
219,188
Factor Arrows
29,594
Factor Arrows
24,797
Factor Arrows
31,599
Factor Arrows
3533
Factor Arrows
1341

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, 13, 41

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 3 x 3 x 13 x 41 = 153,504

This can also be written as 25 x 32 x 131 x 411 = 153,504

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


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