Q: What are the prime factors of the number 262,146,213?

 A: 3, 7, 47, 1093

Why are those the prime factors of the number 262,146,213?

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 262,146,213

262,146,213
Factor Arrows
387,382,071
Factor Arrows
329,127,357
Factor Arrows
39,709,119
Factor Arrows
33,236,373
Factor Arrows
31,078,791
Factor Arrows
3359,597
Factor Arrows
751,371
Factor Arrows
471,093

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:

3, 7, 47, 1093

We can check our work by multiplying all of the prime factors together: 3 x 3 x 3 x 3 x 3 x 3 x 7 x 47 x 1,093 = 262,146,213

This can also be written as 36 x 71 x 471 x 1,0931 = 262,146,213

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


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