Q: What are the prime factors of the number 393,193?

Why are those the prime factors of the number 393,193?

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 393,193

	393,193
17		23,129
	101		229

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:

17, 101, 229

We can check our work by multiplying all of the prime factors together: 17 x 101 x 229 = 393,193

This can also be written as 17¹ x 101¹ x 229¹ = 393,193

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

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