What is the greatest common divisor of 234 and 585?

Answer 1

117.

First, find the prime factorization for 234 and for 585. It may be helpful to include all prime numbers up to the highest factor in the listed factorization, even if a particular Prime number has to be listed as to the zero power:

234 = 2 x 32 x 13 = 21 x 32 x 50 x 70 x 110 x 131

585 = 32 x 5 x 13 = 20 x 32 x 51 x 70 x 110 x 131

Then, to find the greatest common divisor, take each factor the fewest number of times that it appears in either factorization. So the greatest common factor will include 20, 32, 50, 70, 110, and 131.

The greatest common factor is thus 20 x 32 x 50 x 70 x 110 x 131 = 117.