Q: What are the prime factors of the number 126,224?

 A: 2, 7, 23

Why are those the prime factors of the number 126,224?

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 126,224

126,224
Factor Arrows
263,112
Factor Arrows
231,556
Factor Arrows
215,778
Factor Arrows
27,889
Factor Arrows
71,127
Factor Arrows
7161
Factor Arrows
723

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, 7, 23

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 7 x 7 x 7 x 23 = 126,224

This can also be written as 24 x 73 x 231 = 126,224

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


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