Q: What are the prime factors of the number 468,114,552?

 A: 2, 3, 19, 193, 197

Why are those the prime factors of the number 468,114,552?

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 468,114,552

468,114,552
Factor Arrows
2234,057,276
Factor Arrows
2117,028,638
Factor Arrows
258,514,319
Factor Arrows
319,504,773
Factor Arrows
36,501,591
Factor Arrows
32,167,197
Factor Arrows
3722,399
Factor Arrows
1938,021
Factor Arrows
193197

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, 19, 193, 197

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 3 x 3 x 3 x 3 x 19 x 193 x 197 = 468,114,552

This can also be written as 23 x 34 x 191 x 1931 x 1971 = 468,114,552

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


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