Q: What are the prime factors of the number 821,808?

 A: 2, 3, 13, 439

Why are those the prime factors of the number 821,808?

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 821,808

821,808
Factor Arrows
2410,904
Factor Arrows
2205,452
Factor Arrows
2102,726
Factor Arrows
251,363
Factor Arrows
317,121
Factor Arrows
35,707
Factor Arrows
13439

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, 13, 439

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 3 x 3 x 13 x 439 = 821,808

This can also be written as 24 x 32 x 131 x 4391 = 821,808

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


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