Q: What are the prime factors of the number 21,742,200?

 A: 2, 3, 5, 47, 257

Why are those the prime factors of the number 21,742,200?

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 21,742,200

21,742,200
Factor Arrows
210,871,100
Factor Arrows
25,435,550
Factor Arrows
22,717,775
Factor Arrows
3905,925
Factor Arrows
3301,975
Factor Arrows
560,395
Factor Arrows
512,079
Factor Arrows
47257

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, 47, 257

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 47 x 257 = 21,742,200

This can also be written as 23 x 32 x 52 x 471 x 2571 = 21,742,200

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


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