Q: What are the prime factors of the number 402,103,359?

 A: 3, 7, 41, 353

Why are those the prime factors of the number 402,103,359?

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 402,103,359

402,103,359
Factor Arrows
3134,034,453
Factor Arrows
344,678,151
Factor Arrows
314,892,717
Factor Arrows
34,964,239
Factor Arrows
7709,177
Factor Arrows
7101,311
Factor Arrows
714,473
Factor Arrows
41353

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:

3, 7, 41, 353

We can check our work by multiplying all of the prime factors together: 3 x 3 x 3 x 3 x 7 x 7 x 7 x 41 x 353 = 402,103,359

This can also be written as 34 x 73 x 411 x 3531 = 402,103,359

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


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