What number goes into 68 and 85?

Answer 1

17.

68/17= 4

85/17= 5

If you want to find the Greatest Common Denominator (the lowest number that goes into a set of numbers) of two numbers like 68 and 85 or more than two numbers for that matter, you first must find the prime factorization of all the numbers.

Prime Factorization means breaking every factor of a certain number down until they are all prime. The best way to find prime factorization is to make a factor tree by starting with the number and breaking each factor pair down further and further. 68/2 gives you the two factors of 2 and 34 (2x34=68) Now, 2 is a Prime number so you are done with that. Break down 34 to get 2 and 17 (2x17=34). 2 and 17 are both prime so you can't go any further. Now you have three prime numbers for your factorization (2,2, and 17).

Prime factorization of 68= 2x2x17

Prime factorization of 85= 5x17

(Notice the factorization equal the number)

Second, take the factors that they all share and multiply them together. In this case, 68 and 85 only have one shared factor (17) so your Greatest Common Denominator is 17.

This method may seem confusing but it helps if your trying to find the GCD of more than 2 numbers. For instance...

Find the Greatest Common Denominator of 204, 112, 36, and 48.

First find the prime factorization for each:

204= 2x2x3x17

112= 2x2x2x2x7

36= 2x2x3x3

48= 2x2x2x2x3

Now find the common factors and multiply them together. They all share:

204= 2x2x3x17

112= 2x2x2x2x7

36= 2x2x3x3

48= 2x2x2x2x3

And so you're left with two 2's. Multiply them together to get:

2x2= 4

4 is your Greatest Common Denominator.