Q: What are the prime factors of the number 414,645,250?

 A: 2, 5, 1201, 1381

Why are those the prime factors of the number 414,645,250?

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 414,645,250

414,645,250
Factor Arrows
2207,322,625
Factor Arrows
541,464,525
Factor Arrows
58,292,905
Factor Arrows
51,658,581
Factor Arrows
1,2011,381

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, 1201, 1381

We can check our work by multiplying all of the prime factors together: 2 x 5 x 5 x 5 x 1,201 x 1,381 = 414,645,250

This can also be written as 21 x 53 x 1,2011 x 1,3811 = 414,645,250

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


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