Q: What are the prime factors of the number 40,206,400?

 A: 2, 5, 13, 1933

Why are those the prime factors of the number 40,206,400?

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 40,206,400

40,206,400
Factor Arrows
220,103,200
Factor Arrows
210,051,600
Factor Arrows
25,025,800
Factor Arrows
22,512,900
Factor Arrows
21,256,450
Factor Arrows
2628,225
Factor Arrows
5125,645
Factor Arrows
525,129
Factor Arrows
131,933

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, 13, 1933

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 13 x 1,933 = 40,206,400

This can also be written as 26 x 52 x 131 x 1,9331 = 40,206,400

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


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