Q: What are the prime factors of the number 735,212,144?

 A: 2, 19, 127, 137, 139

Why are those the prime factors of the number 735,212,144?

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 735,212,144

735,212,144
Factor Arrows
2367,606,072
Factor Arrows
2183,803,036
Factor Arrows
291,901,518
Factor Arrows
245,950,759
Factor Arrows
192,418,461
Factor Arrows
12719,043
Factor Arrows
137139

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, 19, 127, 137, 139

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 19 x 127 x 137 x 139 = 735,212,144

This can also be written as 24 x 191 x 1271 x 1371 x 1391 = 735,212,144

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


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