Q: What are the prime factors of the number 34,413,120?

 A: 2, 3, 5, 7, 569

Why are those the prime factors of the number 34,413,120?

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 34,413,120

34,413,120
Factor Arrows
217,206,560
Factor Arrows
28,603,280
Factor Arrows
24,301,640
Factor Arrows
22,150,820
Factor Arrows
21,075,410
Factor Arrows
2537,705
Factor Arrows
3179,235
Factor Arrows
359,745
Factor Arrows
319,915
Factor Arrows
53,983
Factor Arrows
7569

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, 5, 7, 569

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 3 x 3 x 3 x 5 x 7 x 569 = 34,413,120

This can also be written as 26 x 33 x 51 x 71 x 5691 = 34,413,120

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


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