Q: What are the prime factors of the number 34,443,000?

 A: 2, 3, 5, 43, 89

Why are those the prime factors of the number 34,443,000?

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 34,443,000

34,443,000
Factor Arrows
217,221,500
Factor Arrows
28,610,750
Factor Arrows
24,305,375
Factor Arrows
31,435,125
Factor Arrows
3478,375
Factor Arrows
595,675
Factor Arrows
519,135
Factor Arrows
53,827
Factor Arrows
4389

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, 5, 43, 89

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5 x 43 x 89 = 34,443,000

This can also be written as 23 x 32 x 53 x 431 x 891 = 34,443,000

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


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