Q: What are the prime factors of the number 346,304,560?

 A: 2, 5, 7, 23, 167

Why are those the prime factors of the number 346,304,560?

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 346,304,560

346,304,560
Factor Arrows
2173,152,280
Factor Arrows
286,576,140
Factor Arrows
243,288,070
Factor Arrows
221,644,035
Factor Arrows
54,328,807
Factor Arrows
7618,401
Factor Arrows
788,343
Factor Arrows
233,841
Factor Arrows
23167

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, 5, 7, 23, 167

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 5 x 7 x 7 x 23 x 23 x 167 = 346,304,560

This can also be written as 24 x 51 x 72 x 232 x 1671 = 346,304,560

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


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