Q: What are the prime factors of the number 105,600,512?

 A: 2, 206251

Why are those the prime factors of the number 105,600,512?

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 105,600,512

105,600,512
Factor Arrows
252,800,256
Factor Arrows
226,400,128
Factor Arrows
213,200,064
Factor Arrows
26,600,032
Factor Arrows
23,300,016
Factor Arrows
21,650,008
Factor Arrows
2825,004
Factor Arrows
2412,502
Factor Arrows
2206,251

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, 206251

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 206,251 = 105,600,512

This can also be written as 29 x 206,2511 = 105,600,512

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


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