Q: What are the prime factors of the number 103,632,144?

 A: 2, 3, 7, 11, 2549

Why are those the prime factors of the number 103,632,144?

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 103,632,144

103,632,144
Factor Arrows
251,816,072
Factor Arrows
225,908,036
Factor Arrows
212,954,018
Factor Arrows
26,477,009
Factor Arrows
32,159,003
Factor Arrows
7308,429
Factor Arrows
1128,039
Factor Arrows
112,549

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, 7, 11, 2549

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 3 x 7 x 11 x 11 x 2,549 = 103,632,144

This can also be written as 24 x 31 x 71 x 112 x 2,5491 = 103,632,144

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


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