What is the GCF of 85 and 51?

Answer 1

To find the greatest common factor between two numbers, we do the following multiple times:

(1) Take the remainder of the larger divided by the smaller

(2) If there is no remaineder, the smaller is the GCF.

(3) Repeat the process with the smaller number and the remainder.

Example: GCF of 18 and 10.

18/10=1 R 8. So, we take the GCF of 8 and 10.

10/8=1 R 2. We take the GCF of 2 and 8.

8/2=4 R 0. By rule #2, 2 is our GCF.

Lets use 85 and 51.

85/51=1 R 34

51/34=1 R 17

34/17=2 R 0.

Our answer is 17.

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Or an easier way to do it is factor trees. 51 85

^ ^

5 17 3 17

The numbers cannot be simplified any more, so there fore the GCF is 17.
Factors of 85:

1,5,17,51

Factors of 51:

1,3,17,51

Therefore, the greatest common factor is 17.
It is: 17