Q: What are the prime factors of the number 152,143,758?

 A: 2, 3, 13, 23, 349

Why are those the prime factors of the number 152,143,758?

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 152,143,758

152,143,758
Factor Arrows
276,071,879
Factor Arrows
325,357,293
Factor Arrows
38,452,431
Factor Arrows
32,817,477
Factor Arrows
3939,159
Factor Arrows
3313,053
Factor Arrows
3104,351
Factor Arrows
138,027
Factor Arrows
23349

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, 23, 349

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 13 x 23 x 349 = 152,143,758

This can also be written as 21 x 36 x 131 x 231 x 3491 = 152,143,758

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


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