Q: What are the prime factors of the number 160,342,016?

 A: 2, 23, 37

Why are those the prime factors of the number 160,342,016?

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 160,342,016

160,342,016
Factor Arrows
280,171,008
Factor Arrows
240,085,504
Factor Arrows
220,042,752
Factor Arrows
210,021,376
Factor Arrows
25,010,688
Factor Arrows
22,505,344
Factor Arrows
21,252,672
Factor Arrows
2626,336
Factor Arrows
2313,168
Factor Arrows
2156,584
Factor Arrows
278,292
Factor Arrows
239,146
Factor Arrows
219,573
Factor Arrows
23851
Factor Arrows
2337

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, 23, 37

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 23 x 23 x 37 = 160,342,016

This can also be written as 213 x 232 x 371 = 160,342,016

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


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