Q: What are the prime factors of the number 320,100,300?

 A: 2, 3, 5, 13, 109, 251

Why are those the prime factors of the number 320,100,300?

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 320,100,300

320,100,300
Factor Arrows
2160,050,150
Factor Arrows
280,025,075
Factor Arrows
326,675,025
Factor Arrows
38,891,675
Factor Arrows
51,778,335
Factor Arrows
5355,667
Factor Arrows
1327,359
Factor Arrows
109251

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, 13, 109, 251

We can check our work by multiplying all of the prime factors together: 2 x 2 x 3 x 3 x 5 x 5 x 13 x 109 x 251 = 320,100,300

This can also be written as 22 x 32 x 52 x 131 x 1091 x 2511 = 320,100,300

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


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