Q: What are the prime factors of the number 218,400?

 A: 2, 3, 5, 7, 13

Why are those the prime factors of the number 218,400?

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 218,400

218,400
Factor Arrows
2109,200
Factor Arrows
254,600
Factor Arrows
227,300
Factor Arrows
213,650
Factor Arrows
26,825
Factor Arrows
32,275
Factor Arrows
5455
Factor Arrows
591
Factor Arrows
713

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, 7, 13

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 5 x 5 x 7 x 13 = 218,400

This can also be written as 25 x 31 x 52 x 71 x 131 = 218,400

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


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