Q: What are the prime factors of the number 154,356,300?

 A: 2, 3, 5, 7, 8167

Why are those the prime factors of the number 154,356,300?

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 154,356,300

154,356,300
Factor Arrows
277,178,150
Factor Arrows
238,589,075
Factor Arrows
312,863,025
Factor Arrows
34,287,675
Factor Arrows
31,429,225
Factor Arrows
5285,845
Factor Arrows
557,169
Factor Arrows
78,167

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, 8167

We can check our work by multiplying all of the prime factors together: 2 x 2 x 3 x 3 x 3 x 5 x 5 x 7 x 8,167 = 154,356,300

This can also be written as 22 x 33 x 52 x 71 x 8,1671 = 154,356,300

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


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