Q: What are the prime factors of the number 785,188,352?

 A: 2, 13, 23, 223

Why are those the prime factors of the number 785,188,352?

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 785,188,352

785,188,352
Factor Arrows
2392,594,176
Factor Arrows
2196,297,088
Factor Arrows
298,148,544
Factor Arrows
249,074,272
Factor Arrows
224,537,136
Factor Arrows
212,268,568
Factor Arrows
26,134,284
Factor Arrows
23,067,142
Factor Arrows
21,533,571
Factor Arrows
13117,967
Factor Arrows
235,129
Factor Arrows
23223

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, 13, 23, 223

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 2 x 2 x 2 x 13 x 23 x 23 x 223 = 785,188,352

This can also be written as 29 x 131 x 232 x 2231 = 785,188,352

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


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