Q: What are the prime factors of the number 300,112,200?

 A: 2, 3, 5, 137, 1217

Why are those the prime factors of the number 300,112,200?

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 300,112,200

300,112,200
Factor Arrows
2150,056,100
Factor Arrows
275,028,050
Factor Arrows
237,514,025
Factor Arrows
312,504,675
Factor Arrows
34,168,225
Factor Arrows
5833,645
Factor Arrows
5166,729
Factor Arrows
1371,217

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, 137, 1217

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 3 x 3 x 5 x 5 x 137 x 1,217 = 300,112,200

This can also be written as 23 x 32 x 52 x 1371 x 1,2171 = 300,112,200

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


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