Q: What are the prime factors of the number 33,522,174?

 A: 2, 3, 7, 41, 103

Why are those the prime factors of the number 33,522,174?

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 33,522,174

33,522,174
Factor Arrows
216,761,087
Factor Arrows
35,587,029
Factor Arrows
31,862,343
Factor Arrows
3620,781
Factor Arrows
3206,927
Factor Arrows
729,561
Factor Arrows
74,223
Factor Arrows
41103

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, 41, 103

We can check our work by multiplying all of the prime factors together: 2 x 3 x 3 x 3 x 3 x 7 x 7 x 41 x 103 = 33,522,174

This can also be written as 21 x 34 x 72 x 411 x 1031 = 33,522,174

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


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