Q: What are the prime factors of the number 135,160,200?

 A: 2, 3, 5, 7, 17, 631

Why are those the prime factors of the number 135,160,200?

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 135,160,200

135,160,200
Factor Arrows
267,580,100
Factor Arrows
233,790,050
Factor Arrows
216,895,025
Factor Arrows
35,631,675
Factor Arrows
31,877,225
Factor Arrows
5375,445
Factor Arrows
575,089
Factor Arrows
710,727
Factor Arrows
17631

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, 17, 631

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 3 x 3 x 5 x 5 x 7 x 17 x 631 = 135,160,200

This can also be written as 23 x 32 x 52 x 71 x 171 x 6311 = 135,160,200

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


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