Q: What are the prime factors of the number 35,003,000?

 A: 2, 5, 17, 29, 71

Why are those the prime factors of the number 35,003,000?

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 35,003,000

35,003,000
Factor Arrows
217,501,500
Factor Arrows
28,750,750
Factor Arrows
24,375,375
Factor Arrows
5875,075
Factor Arrows
5175,015
Factor Arrows
535,003
Factor Arrows
172,059
Factor Arrows
2971

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, 5, 17, 29, 71

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 5 x 5 x 5 x 17 x 29 x 71 = 35,003,000

This can also be written as 23 x 53 x 171 x 291 x 711 = 35,003,000

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


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