Q: What are the prime factors of the number 735,816?

 A: 2, 3, 23, 31, 43

Why are those the prime factors of the number 735,816?

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 735,816

735,816
Factor Arrows
2367,908
Factor Arrows
2183,954
Factor Arrows
291,977
Factor Arrows
330,659
Factor Arrows
231,333
Factor Arrows
3143

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, 23, 31, 43

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 3 x 23 x 31 x 43 = 735,816

This can also be written as 23 x 31 x 231 x 311 x 431 = 735,816

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


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