Q: What are the prime factors of the number 31,401,000?

 A: 2, 3, 5, 1163

Why are those the prime factors of the number 31,401,000?

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 31,401,000

31,401,000
Factor Arrows
215,700,500
Factor Arrows
27,850,250
Factor Arrows
23,925,125
Factor Arrows
31,308,375
Factor Arrows
3436,125
Factor Arrows
3145,375
Factor Arrows
529,075
Factor Arrows
55,815
Factor Arrows
51,163

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, 5, 1163

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 5 x 5 x 5 x 1,163 = 31,401,000

This can also be written as 23 x 33 x 53 x 1,1631 = 31,401,000

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


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