Q: What are the prime factors of the number 144,204,200?

 A: 2, 5, 7, 17, 73, 83

Why are those the prime factors of the number 144,204,200?

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 144,204,200

144,204,200
Factor Arrows
272,102,100
Factor Arrows
236,051,050
Factor Arrows
218,025,525
Factor Arrows
53,605,105
Factor Arrows
5721,021
Factor Arrows
7103,003
Factor Arrows
176,059
Factor Arrows
7383

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, 5, 7, 17, 73, 83

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 5 x 5 x 7 x 17 x 73 x 83 = 144,204,200

This can also be written as 23 x 52 x 71 x 171 x 731 x 831 = 144,204,200

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


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