Q: What are the prime factors of the number 46,457,152?

 A: 2, 7, 103699

Why are those the prime factors of the number 46,457,152?

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 46,457,152

46,457,152
Factor Arrows
223,228,576
Factor Arrows
211,614,288
Factor Arrows
25,807,144
Factor Arrows
22,903,572
Factor Arrows
21,451,786
Factor Arrows
2725,893
Factor Arrows
7103,699

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, 7, 103699

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 7 x 103,699 = 46,457,152

This can also be written as 26 x 71 x 103,6991 = 46,457,152

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


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