Question

En una granja hay 72 ovejas y 84 cabras .¿cómo se puede repartir a los animales en cercados del mayor tamaño posible , pero sin mezclar , de forma que en todos haya el mismo número de animales?

Answer 1

The animals must be separated in groups of 12.

Explanation:

To answer this problem, these quantities must be decomposed into their prime factors.

`72/2 = 36\\36/2 = 18\\2/18 = 9\\9/3 = 3\\3/3 = 1\\2 ^ 3 * 3 ^ 2 = 72\\`

`84/2 = 42\\42/2 = 21\\21/3 = 7\\7/7 = 1\\2 ^ 2 * 3 * 7 = 82\\`

Now we look for the maximum common divisor between both terms to find the number that allows us to divide both the quantities into groups of equal size

Then the largest common divisor between 72 and 84 is equal to the common terms with its lowest exponent

mcd (72; 84) =
`2 ^ 2 * 3\\`

mcd (72; 84) = 12

Then the animals should be separated into groups of 12.

This means that 6 fences should be made with 12 sheep in each and 7 fences with 12 goats in each.