Q: What are the prime factors of the number 42,301,224?

 A: 2, 3, 7, 101, 277

Why are those the prime factors of the number 42,301,224?

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 42,301,224

42,301,224
Factor Arrows
221,150,612
Factor Arrows
210,575,306
Factor Arrows
25,287,653
Factor Arrows
31,762,551
Factor Arrows
3587,517
Factor Arrows
3195,839
Factor Arrows
727,977
Factor Arrows
101277

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, 101, 277

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 3 x 3 x 3 x 7 x 101 x 277 = 42,301,224

This can also be written as 23 x 33 x 71 x 1011 x 2771 = 42,301,224

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


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