Q: What are the prime factors of the number 346,112,160?

 A: 2, 3, 5, 41, 43, 409

Why are those the prime factors of the number 346,112,160?

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 346,112,160

346,112,160
Factor Arrows
2173,056,080
Factor Arrows
286,528,040
Factor Arrows
243,264,020
Factor Arrows
221,632,010
Factor Arrows
210,816,005
Factor Arrows
33,605,335
Factor Arrows
5721,067
Factor Arrows
4117,587
Factor Arrows
43409

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, 41, 43, 409

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 3 x 5 x 41 x 43 x 409 = 346,112,160

This can also be written as 25 x 31 x 51 x 411 x 431 x 4091 = 346,112,160

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


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