Q: What are the prime factors of the number 4,600,400?

 A: 2, 5, 7, 31, 53

Why are those the prime factors of the number 4,600,400?

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 4,600,400

4,600,400
Factor Arrows
22,300,200
Factor Arrows
21,150,100
Factor Arrows
2575,050
Factor Arrows
2287,525
Factor Arrows
557,505
Factor Arrows
511,501
Factor Arrows
71,643
Factor Arrows
3153

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, 31, 53

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 5 x 5 x 7 x 31 x 53 = 4,600,400

This can also be written as 24 x 52 x 71 x 311 x 531 = 4,600,400

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


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