Q: What are the prime factors of the number 5,978,304?

 A: 2, 3, 97, 107

Why are those the prime factors of the number 5,978,304?

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 5,978,304

5,978,304
Factor Arrows
22,989,152
Factor Arrows
21,494,576
Factor Arrows
2747,288
Factor Arrows
2373,644
Factor Arrows
2186,822
Factor Arrows
293,411
Factor Arrows
331,137
Factor Arrows
310,379
Factor Arrows
97107

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, 97, 107

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 97 x 107 = 5,978,304

This can also be written as 26 x 32 x 971 x 1071 = 5,978,304

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


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