Q: What are the prime factors of the number 349,408?

 A: 2, 61, 179

Why are those the prime factors of the number 349,408?

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 349,408

349,408
Factor Arrows
2174,704
Factor Arrows
287,352
Factor Arrows
243,676
Factor Arrows
221,838
Factor Arrows
210,919
Factor Arrows
61179

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, 61, 179

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 61 x 179 = 349,408

This can also be written as 25 x 611 x 1791 = 349,408

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


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