Q: What are the prime factors of the number 3,305,344?

 A: 2, 7, 17, 31

Why are those the prime factors of the number 3,305,344?

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 3,305,344

3,305,344
Factor Arrows
21,652,672
Factor Arrows
2826,336
Factor Arrows
2413,168
Factor Arrows
2206,584
Factor Arrows
2103,292
Factor Arrows
251,646
Factor Arrows
225,823
Factor Arrows
73,689
Factor Arrows
7527
Factor Arrows
1731

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, 7, 17, 31

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7 x 17 x 31 = 3,305,344

This can also be written as 27 x 72 x 171 x 311 = 3,305,344

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


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