Q: What are the prime factors of the number 813,653,865?

 A: 3, 5, 23, 37, 21247

Why are those the prime factors of the number 813,653,865?

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 813,653,865

813,653,865
Factor Arrows
3271,217,955
Factor Arrows
390,405,985
Factor Arrows
518,081,197
Factor Arrows
23786,139
Factor Arrows
3721,247

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, 5, 23, 37, 21247

We can check our work by multiplying all of the prime factors together: 3 x 3 x 5 x 23 x 37 x 21,247 = 813,653,865

This can also be written as 32 x 51 x 231 x 371 x 21,2471 = 813,653,865

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


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