Q: What are the prime factors of the number 103,620,300?

 A: 2, 3, 5, 7, 19, 53

Why are those the prime factors of the number 103,620,300?

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 103,620,300

103,620,300
Factor Arrows
251,810,150
Factor Arrows
225,905,075
Factor Arrows
38,635,025
Factor Arrows
51,727,005
Factor Arrows
5345,401
Factor Arrows
749,343
Factor Arrows
77,049
Factor Arrows
71,007
Factor Arrows
1953

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, 19, 53

We can check our work by multiplying all of the prime factors together: 2 x 2 x 3 x 5 x 5 x 7 x 7 x 7 x 19 x 53 = 103,620,300

This can also be written as 22 x 31 x 52 x 73 x 191 x 531 = 103,620,300

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


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