Q: What are the prime factors of the number 23,323,200?

 A: 2, 3, 5, 43, 113

Why are those the prime factors of the number 23,323,200?

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 23,323,200

23,323,200
Factor Arrows
211,661,600
Factor Arrows
25,830,800
Factor Arrows
22,915,400
Factor Arrows
21,457,700
Factor Arrows
2728,850
Factor Arrows
2364,425
Factor Arrows
3121,475
Factor Arrows
524,295
Factor Arrows
54,859
Factor Arrows
43113

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, 43, 113

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 3 x 5 x 5 x 43 x 113 = 23,323,200

This can also be written as 26 x 31 x 52 x 431 x 1131 = 23,323,200

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


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