Q: What are the prime factors of the number 315,066,400?

 A: 2, 5, 11, 35803

Why are those the prime factors of the number 315,066,400?

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 315,066,400

315,066,400
Factor Arrows
2157,533,200
Factor Arrows
278,766,600
Factor Arrows
239,383,300
Factor Arrows
219,691,650
Factor Arrows
29,845,825
Factor Arrows
51,969,165
Factor Arrows
5393,833
Factor Arrows
1135,803

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, 11, 35803

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 5 x 5 x 11 x 35,803 = 315,066,400

This can also be written as 25 x 52 x 111 x 35,8031 = 315,066,400

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


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