Q: What are the prime factors of the number 240,200,400?

 A: 2, 3, 5, 11, 31, 587

Why are those the prime factors of the number 240,200,400?

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 240,200,400

240,200,400
Factor Arrows
2120,100,200
Factor Arrows
260,050,100
Factor Arrows
230,025,050
Factor Arrows
215,012,525
Factor Arrows
35,004,175
Factor Arrows
51,000,835
Factor Arrows
5200,167
Factor Arrows
1118,197
Factor Arrows
31587

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, 11, 31, 587

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 3 x 5 x 5 x 11 x 31 x 587 = 240,200,400

This can also be written as 24 x 31 x 52 x 111 x 311 x 5871 = 240,200,400

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


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