Q: What are the prime factors of the number 737,184?

 A: 2, 3, 7, 1097

Why are those the prime factors of the number 737,184?

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 737,184

737,184
Factor Arrows
2368,592
Factor Arrows
2184,296
Factor Arrows
292,148
Factor Arrows
246,074
Factor Arrows
223,037
Factor Arrows
37,679
Factor Arrows
71,097

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, 7, 1097

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 3 x 7 x 1,097 = 737,184

This can also be written as 25 x 31 x 71 x 1,0971 = 737,184

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


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