Q: What are the prime factors of the number 205,650,648?

 A: 2, 3, 7, 71, 821

Why are those the prime factors of the number 205,650,648?

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 205,650,648

205,650,648
Factor Arrows
2102,825,324
Factor Arrows
251,412,662
Factor Arrows
225,706,331
Factor Arrows
38,568,777
Factor Arrows
32,856,259
Factor Arrows
7408,037
Factor Arrows
758,291
Factor Arrows
71821

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, 7, 71, 821

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 3 x 3 x 7 x 7 x 71 x 821 = 205,650,648

This can also be written as 23 x 32 x 72 x 711 x 8211 = 205,650,648

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


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