Question

A box of chocolates has 24 chocolates. How many ways could all 24 chocolates be shared equally? What is the greatest number of people who could have an equal share of 24 chocolates or 36 chocolates?

a) 24 chocolates can be shared equally in 24 different ways.
b) 24 chocolates can be shared equally in 12 different ways.
c) 36 chocolates can be shared equally in 9 different ways.
d) The greatest number of people who can have an equal share of 24 chocolates or 36 chocolates is 6

Answer 1

There are 8 different ways to equally share 24 chocolates, and the greatest number of people who can have an equal share of either 24 or 36 chocolates is 12.

Step-by-step explanation:

In Mathematics, we often deal with questions of how to share or distribute items evenly among a certain number of people. When we have a box of chocolates that contains 24 chocolates, we want to find all the possible ways these chocolates can be shared equally among different numbers of people. An equal share means that each person gets the same number of chocolates without any chocolates left over.

To find all the different sharing possibilities, we look for all the divisors of 24. These are 1, 2, 3, 4, 6, 8, 12, and 24. So, there are 8 different ways to share 24 chocolates equally among people. Now, if we want to find out the greatest number of people who can have an equal share of either 24 or 36 chocolates, we need to find the lowest common multiple (LCM) of these two numbers. The divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The greatest common divisor that 24 and 36 share is 12. Therefore, the greatest number of people who can have an equal share of either 24 chocolates or 36 chocolates is 12.