Q: What are the prime factors of the number 34,204,400?

 A: 2, 5, 233, 367

Why are those the prime factors of the number 34,204,400?

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 34,204,400

34,204,400
Factor Arrows
217,102,200
Factor Arrows
28,551,100
Factor Arrows
24,275,550
Factor Arrows
22,137,775
Factor Arrows
5427,555
Factor Arrows
585,511
Factor Arrows
233367

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, 233, 367

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 5 x 5 x 233 x 367 = 34,204,400

This can also be written as 24 x 52 x 2331 x 3671 = 34,204,400

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


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