Question

A class of $ 18 $ girls and $ 24 $ boys is divided into groups such that all groups have the same number of girls and boys and no one is left out. What is the greatest number of groups possible?

Answer 1

Hint: To get the exact number of girls and boys in each of the group, first we will find the Highest common factor between both the number of girls and the boys by finding the prime factors and then will identify the greatest number of possible groups.


Complete step-by-step solution:
Given that:
 $ 18 $ girls
 $ 24 $ boys
Find the prime factors of the numbers of girls and boys
Girls $ = 18 = 2 \times 3 \times 3 $
Boys $ = 24 = 2 \times 2 \times 2 \times 3 $
Now find the highest common factor from the above two expression –
The highest common factor is the common factor present in both the expression, here it is the number
Now, to get the number of girls and boys going to be in each group we will divide the total number of girls and boys by the number by
Girls per group $ = \dfrac{{12}}{3} = 4 $
Boys per group $ = \dfrac{{15}}{3} = 5 $

Hence, there will be three highest possible groups with four girls and five boys in each group.


Note: LCM (Least Common Multiple) can be defined as the least or the smallest number with which the given numbers are exactly divisible. It is also known as the least common divisor. LCM can be well defined as the product of constant and HCF. Always read the given data and frame the mathematical expressions accordingly and get the required value. Be clear between the highest common factor and the least common multiple and apply it accordingly.