Q: What are the prime factors of the number 146,400,210?

 A: 2, 3, 5, 11, 5477

Why are those the prime factors of the number 146,400,210?

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 146,400,210

146,400,210
Factor Arrows
273,200,105
Factor Arrows
324,400,035
Factor Arrows
38,133,345
Factor Arrows
32,711,115
Factor Arrows
3903,705
Factor Arrows
3301,235
Factor Arrows
560,247
Factor Arrows
115,477

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, 11, 5477

We can check our work by multiplying all of the prime factors together: 2 x 3 x 3 x 3 x 3 x 3 x 5 x 11 x 5,477 = 146,400,210

This can also be written as 21 x 35 x 51 x 111 x 5,4771 = 146,400,210

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


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