Q: What are the prime factors of the number 312,244,100?

 A: 2, 5, 7, 17, 19, 1381

Why are those the prime factors of the number 312,244,100?

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 312,244,100

312,244,100
Factor Arrows
2156,122,050
Factor Arrows
278,061,025
Factor Arrows
515,612,205
Factor Arrows
53,122,441
Factor Arrows
7446,063
Factor Arrows
1726,239
Factor Arrows
191,381

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, 17, 19, 1381

We can check our work by multiplying all of the prime factors together: 2 x 2 x 5 x 5 x 7 x 17 x 19 x 1,381 = 312,244,100

This can also be written as 22 x 52 x 71 x 171 x 191 x 1,3811 = 312,244,100

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


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