Q: What are the prime factors of the number 213,705,121?

 A: 7, 23, 103, 263

Why are those the prime factors of the number 213,705,121?

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 213,705,121

213,705,121
Factor Arrows
730,529,303
Factor Arrows
74,361,329
Factor Arrows
7623,047
Factor Arrows
2327,089
Factor Arrows
103263

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:

7, 23, 103, 263

We can check our work by multiplying all of the prime factors together: 7 x 7 x 7 x 23 x 103 x 263 = 213,705,121

This can also be written as 73 x 231 x 1031 x 2631 = 213,705,121

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


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