There are 17 animals in the barn. Some are chickens and some are cows. There are 56 legs in all. How many of each animal are there?

6 chickens, 11 cows.

Step-by-step explanation:

x - chickens

y - cows

x + y = 17

2x + 4y = 56   <-- chickens have 2 legs, cows have 4.

y = -x + 17

Substitute (-x+17) for y in the second equation.

2x  + 4(-x + 17) = 56

2x -4x + 68 = 56

2x = 12

x = 6 chickens

Now substitute 6 for x

6 + y = 17

y = 11 cows

For this case we have that by definition, the GFC of two numbers is the largest number that is a factor of both numbers.

We have the following expression:

This can be rewritten as:

It is observed that if we take common factor, the largest factor will be given by

Thus, the GFC of the given expression is 27

27