Q: What are the prime factors of the number 42,264,320?

 A: 2, 5, 7, 53, 89

Why are those the prime factors of the number 42,264,320?

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 42,264,320

42,264,320
Factor Arrows
221,132,160
Factor Arrows
210,566,080
Factor Arrows
25,283,040
Factor Arrows
22,641,520
Factor Arrows
21,320,760
Factor Arrows
2660,380
Factor Arrows
2330,190
Factor Arrows
2165,095
Factor Arrows
533,019
Factor Arrows
74,717
Factor Arrows
5389

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, 7, 53, 89

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 7 x 53 x 89 = 42,264,320

This can also be written as 28 x 51 x 71 x 531 x 891 = 42,264,320

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


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