A physical education teacher has to distribute 96 bats and 180 balls among a number of players, such that all players get the same number of bats and, likewise, all players get the same number of balls. What will be the greatest number of players receiving the gift?

Correct option is B

Given:

96 bats

180 balls

We need to find the greatest number of players who can receive the same number of bats and balls.

Solution:

GCD of 96 and 180

We use the Euclidean algorithm to find the GCD:

Divide 180 by 96:

​$$180 \div 96 = 1 \text{ (quotient)} \quad \text{remainder} = 180 - 96 = 84$$​​

Now, divide 96 by 84:

​$$96 \div 84 = 1 \text{ (quotient)} \quad \text{remainder} = 96 - 84 = 12$$​​

Now, divide 84 by 12:

$$84 \div 12 = 7 \text{ (quotient)} \quad \text{remainder} = 84 - 7 \times 12 = 0$$​

The greatest number of players who can receive the same number of bats and balls is 12.