Q: What are the prime factors of the number 414,450?

 A: 2, 3, 5, 307

Why are those the prime factors of the number 414,450?

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 414,450

414,450
Factor Arrows
2207,225
Factor Arrows
369,075
Factor Arrows
323,025
Factor Arrows
37,675
Factor Arrows
51,535
Factor Arrows
5307

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, 307

We can check our work by multiplying all of the prime factors together: 2 x 3 x 3 x 3 x 5 x 5 x 307 = 414,450

This can also be written as 21 x 33 x 52 x 3071 = 414,450

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


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