Question

A physical education teacher wishes to distribute 60 balls and 135 bats equally among a number of boys .The greater number receiving the gift in this way are :___________

Answer 1

To distribute 60 balls and 135 bats equally among a number of boys, you need to find the greatest common divisor (GCD) of 60 and 135. The GCD represents the largest number of boys you can distribute the gifts to equally.

First, find the prime factors of 60 and 135:

- Prime factors of 60: 2^2 * 3 * 5

- Prime factors of 135: 3^3 * 5

Now, find the common factors between the prime factorizations:

- The common factor for 2 is 2^2 (because 60 has it).

- The common factor for 3 is 3 (because both numbers have it).

- The common factor for 5 is 5 (because both numbers have it).

Now, calculate the GCD by multiplying these common factors:

GCD = 2^2 * 3 * 5 = 4 * 3 * 5 = 60

So, the greatest number of boys who can receive the gifts equally is 60.

Step-by-step explanation: