Q: What are the prime factors of the number 120,303,144?

 A: 2, 3, 13, 14281

Why are those the prime factors of the number 120,303,144?

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 120,303,144

120,303,144
Factor Arrows
260,151,572
Factor Arrows
230,075,786
Factor Arrows
215,037,893
Factor Arrows
35,012,631
Factor Arrows
31,670,877
Factor Arrows
3556,959
Factor Arrows
3185,653
Factor Arrows
1314,281

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, 13, 14281

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 3 x 3 x 3 x 3 x 13 x 14,281 = 120,303,144

This can also be written as 23 x 34 x 131 x 14,2811 = 120,303,144

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


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