Question

Judith is planning a party for her younger brother. She has 36 prizes and 24 balloons. What is the greatest number of children who can attend the party so that each child gets an equal number of prizes and an equal number of balloons? How many prizes and balloons will each student receive?

Answer 1

The greatest number of children who can attend Judith's party and receive an equal number of prizes and balloons is 12, with each child getting 3 prizes and 2 balloons.

Step-by-step explanation:

The subject of the question is Mathematics, specifically dealing with finding the greatest common divisor (GCD). Judith wants to distribute 36 prizes and 24 balloons equally among a certain number of children at a party. To find the greatest number of children who can attend and receive an equal number of prizes and balloons, we need to calculate the GCD of 36 and 24.

Using the Euclidean algorithm or prime factorization, we find that the GCD of 36 and 24 is 12. This means Judith can invite a maximum of 12 children to the party. Each child will then receive 36 divided by 12, which is 3 prizes, and 24 divided by 12, which is 2 balloons.

Here are the steps to find the GCD:

1. List the prime factors of each number:
   36 = 2² × 3²
   24 = 2³ × 3
2. Identify the common prime factors and their lowest powers:
   Common prime factors are 2 and 3, with the lowest powers being 2² and 3.
3. Multiply these together to get the GCD:
   2² × 3 = 4 × 3 = 12