Q: What are the prime factors of the number 30,131,200?

 A: 2, 5, 11, 107

Why are those the prime factors of the number 30,131,200?

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 30,131,200

30,131,200
Factor Arrows
215,065,600
Factor Arrows
27,532,800
Factor Arrows
23,766,400
Factor Arrows
21,883,200
Factor Arrows
2941,600
Factor Arrows
2470,800
Factor Arrows
2235,400
Factor Arrows
2117,700
Factor Arrows
258,850
Factor Arrows
229,425
Factor Arrows
55,885
Factor Arrows
51,177
Factor Arrows
11107

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, 5, 11, 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 2 x 2 x 2 x 2 x 5 x 5 x 11 x 107 = 30,131,200

This can also be written as 210 x 52 x 111 x 1071 = 30,131,200

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


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