Q: What are the prime factors of the number 55,166,400?

 A: 2, 3, 5, 1277

Why are those the prime factors of the number 55,166,400?

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 55,166,400

55,166,400
Factor Arrows
227,583,200
Factor Arrows
213,791,600
Factor Arrows
26,895,800
Factor Arrows
23,447,900
Factor Arrows
21,723,950
Factor Arrows
2861,975
Factor Arrows
3287,325
Factor Arrows
395,775
Factor Arrows
331,925
Factor Arrows
56,385
Factor Arrows
51,277

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, 1277

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 3 x 3 x 3 x 5 x 5 x 1,277 = 55,166,400

This can also be written as 26 x 33 x 52 x 1,2771 = 55,166,400

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


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