In the figure below, cd bisects

in order to find the gcf of two numbers, first you need to find the prime factorization of each of the numbers. after you divide out the numbers as much as you can, you get:

36 = 2x2x3x3

84 = 2x2x3x7

from there, you can see which prime factors the two numbers have in common: 2, 2, and 3. then, you multiply the factors together to get 2x2x3=12.

you can double check this by dividing the two initial numbers by 12 to make sure 12 is a factor of them:

36/12 = 3

84/12 = 7

in your explanation, you pretty much give the definition of greatest common factors: that out of all the whole factors that 36 and 84 have in common, 12 has the greatest value.

hope this !