Q: What are the prime factors of the number 35,735,148?

 A: 2, 3, 409, 809

Why are those the prime factors of the number 35,735,148?

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 35,735,148

35,735,148
Factor Arrows
217,867,574
Factor Arrows
28,933,787
Factor Arrows
32,977,929
Factor Arrows
3992,643
Factor Arrows
3330,881
Factor Arrows
409809

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, 409, 809

We can check our work by multiplying all of the prime factors together: 2 x 2 x 3 x 3 x 3 x 409 x 809 = 35,735,148

This can also be written as 22 x 33 x 4091 x 8091 = 35,735,148

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


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