Q: What are the prime factors of the number 542,208?

 A: 2, 3, 353

Why are those the prime factors of the number 542,208?

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 542,208

542,208
Factor Arrows
2271,104
Factor Arrows
2135,552
Factor Arrows
267,776
Factor Arrows
233,888
Factor Arrows
216,944
Factor Arrows
28,472
Factor Arrows
24,236
Factor Arrows
22,118
Factor Arrows
21,059
Factor Arrows
3353

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, 353

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 2 x 2 x 2 x 3 x 353 = 542,208

This can also be written as 29 x 31 x 3531 = 542,208

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


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