Question

Murphy purchases two bags of rice of weights 56 kg and 72 kg. Find the maximum value of weight which can measure the weight of the rice exact number of times.

Answer 1

8

Explanation:

In order to answer this question we need to find the greatest common divisor of the two quantities which will give us the maximum number by which both can be divided.

The greatest common divisor of a group of integers is the largest common divisor that divides each of the integers. The first step to find it is write down the integers as a product of primes, so we have:

`56=(28)(2)=(14)(2)(2)=(7)(2)(2)(2)= 2^3`·
`7`

`72=(24)(3)=8(3)(3)=2^3`·
`3^2`

Now, in order to find the gcd we are going to take the factors that they have in common. In this case they both share the
`2^3`.

Thus,
`2^3=8` is the greatest common divisor and therefore the maximum value of weight which can measure the weight of the rice exact number of times.