Q: What are the prime factors of the number 340,704?

 A: 2, 3, 7, 13

Why are those the prime factors of the number 340,704?

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 340,704

340,704
Factor Arrows
2170,352
Factor Arrows
285,176
Factor Arrows
242,588
Factor Arrows
221,294
Factor Arrows
210,647
Factor Arrows
33,549
Factor Arrows
31,183
Factor Arrows
7169
Factor Arrows
1313

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, 7, 13

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 3 x 7 x 13 x 13 = 340,704

This can also be written as 25 x 32 x 71 x 132 = 340,704

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


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