Q: What are the prime factors of the number 203,435,008?

 A: 2, 7, 101, 281

Why are those the prime factors of the number 203,435,008?

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 203,435,008

203,435,008
Factor Arrows
2101,717,504
Factor Arrows
250,858,752
Factor Arrows
225,429,376
Factor Arrows
212,714,688
Factor Arrows
26,357,344
Factor Arrows
23,178,672
Factor Arrows
21,589,336
Factor Arrows
2794,668
Factor Arrows
2397,334
Factor Arrows
2198,667
Factor Arrows
728,381
Factor Arrows
101281

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, 7, 101, 281

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 7 x 101 x 281 = 203,435,008

This can also be written as 210 x 71 x 1011 x 2811 = 203,435,008

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


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