Q: What are the prime factors of the number 538,002?

 A: 2, 3, 41

Why are those the prime factors of the number 538,002?

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 538,002

538,002
Factor Arrows
2269,001
Factor Arrows
389,667
Factor Arrows
329,889
Factor Arrows
39,963
Factor Arrows
33,321
Factor Arrows
31,107
Factor Arrows
3369
Factor Arrows
3123
Factor Arrows
341

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, 41

We can check our work by multiplying all of the prime factors together: 2 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 41 = 538,002

This can also be written as 21 x 38 x 411 = 538,002

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


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