Judith is planning a party for her younger brother. She has 36 prizes and 24 balloons. What is the greatest number of children she can have at the party so that each child gets an equal number of prizes and an equal number of balloons? Explain your answer.
GCF(36,24) = 12
so, 12 sets of 3 prizes and 2 balloons
229
deez nuts
To find the greatest number of children that Judith can have at the party so that each child gets an equal number of prizes and an equal number of balloons, we need to find the greatest common divisor (GCD) of the number of prizes and the number of balloons.
Step 1: Find the GCD of 36 and 24.
There are several methods to find the GCD, but one common method is to use the Euclidean algorithm.
In this case, we can start by dividing the bigger number (36) by the smaller number (24):
36 ÷ 24 = 1 remainder 12
Then we divide the divisor of the previous step (24) by the remainder (12):
24 ÷ 12 = 2 remainder 0
Since the remainder is 0, we stop. The GCD of 36 and 24 is the divisor of the last step, which is 12.
Step 2: Calculate the number of children.
Since each child should get an equal number of prizes and an equal number of balloons, the number of children should be a divisor of both 36 and 24.
Dividing 36 by the GCD (12) gives us:
36 ÷ 12 = 3
Dividing 24 by the GCD (12) also gives us:
24 ÷ 12 = 2
Therefore, the greatest number of children Judith can have at the party is 2 (since she only has 2 sets of prizes and balloons that can be divided equally among the children).