Q: What are the prime factors of the number 403,213,404?

 A: 2, 3, 11, 31, 211, 467

Why are those the prime factors of the number 403,213,404?

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 403,213,404

403,213,404
Factor Arrows
2201,606,702
Factor Arrows
2100,803,351
Factor Arrows
333,601,117
Factor Arrows
113,054,647
Factor Arrows
3198,537
Factor Arrows
211467

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, 11, 31, 211, 467

We can check our work by multiplying all of the prime factors together: 2 x 2 x 3 x 11 x 31 x 211 x 467 = 403,213,404

This can also be written as 22 x 31 x 111 x 311 x 2111 x 4671 = 403,213,404

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


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