Q: What are the prime factors of the number 364,122,200?

 A: 2, 5, 13, 23, 6089

Why are those the prime factors of the number 364,122,200?

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 364,122,200

364,122,200
Factor Arrows
2182,061,100
Factor Arrows
291,030,550
Factor Arrows
245,515,275
Factor Arrows
59,103,055
Factor Arrows
51,820,611
Factor Arrows
13140,047
Factor Arrows
236,089

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, 13, 23, 6089

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 5 x 5 x 13 x 23 x 6,089 = 364,122,200

This can also be written as 23 x 52 x 131 x 231 x 6,0891 = 364,122,200

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


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