Q: What are the prime factors of the number 314,442,240?

 A: 2, 3, 5, 7, 5849

Why are those the prime factors of the number 314,442,240?

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 314,442,240

314,442,240
Factor Arrows
2157,221,120
Factor Arrows
278,610,560
Factor Arrows
239,305,280
Factor Arrows
219,652,640
Factor Arrows
29,826,320
Factor Arrows
24,913,160
Factor Arrows
22,456,580
Factor Arrows
21,228,290
Factor Arrows
2614,145
Factor Arrows
3204,715
Factor Arrows
540,943
Factor Arrows
75,849

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, 5849

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 2 x 3 x 5 x 7 x 5,849 = 314,442,240

This can also be written as 29 x 31 x 51 x 71 x 5,8491 = 314,442,240

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


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