Q: What are the prime factors of the number 49,152?

 A: 2, 3

Why are those the prime factors of the number 49,152?

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 49,152

49,152
Factor Arrows
224,576
Factor Arrows
212,288
Factor Arrows
26,144
Factor Arrows
23,072
Factor Arrows
21,536
Factor Arrows
2768
Factor Arrows
2384
Factor Arrows
2192
Factor Arrows
296
Factor Arrows
248
Factor Arrows
224
Factor Arrows
212
Factor Arrows
26
Factor Arrows
23

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

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 = 49,152

This can also be written as 214 x 31 = 49,152

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


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