Q: What are the prime factors of the number 123,332,400?

 A: 2, 3, 5, 34259

Why are those the prime factors of the number 123,332,400?

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 123,332,400

123,332,400
Factor Arrows
261,666,200
Factor Arrows
230,833,100
Factor Arrows
215,416,550
Factor Arrows
27,708,275
Factor Arrows
32,569,425
Factor Arrows
3856,475
Factor Arrows
5171,295
Factor Arrows
534,259

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, 34259

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 34,259 = 123,332,400

This can also be written as 24 x 32 x 52 x 34,2591 = 123,332,400

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


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