David wants to give away his collection of 80 green and 62 yellow marbles. If he is going to share them between his friends so that each friend has the same number of marbles of each colour, what is the greatest number of friends he can give his marbles to?
In order to solve this, we need to work out the highest common factor of 62 and 80 as he needs to be able to share the 80 green marbles and the 62 yellow marbles equally. The only factors of 62 are one, two, 31, and 62. The factors of 80 are one, two, four, five, eight, 10, 16, 20, 40, and 80. There are two common factors, one and two. The highest of these is two. Therefore, the highest common factor of 62 and 80 is equal to two.
This means that the greatest number of friends that David can give his marbles to is two.