Chapter 5, Problem 1RE

In Exercises 1 and 2, determine whether the number is divisible by each of the following numbers 2, 3, 4, 5, 6, 8, 9, and 10.

1. 94, 380

To determine

Whether the number 94,380 is divisible by the numbers 2, 3, 4, 5, 6, 8, 9 and 10.

Answer to Problem 1RE

The number 94,380 is divisible by 2, 3, 4, 5, 6 and 10.

Explanation of Solution

By the rules of divisibility, all even numbers divisible by 2.

The given number 94,380 is an even number. Hence, it is divisible by 2.

A number is divisible by 3, if the sum of the digits of the number is divisible by 3.

The sum of the digits of the number 94,380 is 24 and 24 is divisible by 3.

Therefore, 94,380 is divisible by 3.

A number is divisible by 4, if the last two digits of the number is divisible by 4.

The last two digits of the given number 94,380 is 80 and it is divisible by 4.

Hence, 94,380 is divisible by 4.

A number is divisible by 5, if the number ends in 0 or 5.

The last digit of the number 94,380 is 0. Therefore, 94,380 is divisible by 5.

A number is divisible by 6, if the number is divisible by both 2 and 3.

The given number 1155 is divisible by both 2 and 3.

Hence, 94,380 is divisible by 6.

A number is divisible by 8, if the last three digits of the number are divisible by 8.

The last three digits of the number 94,380 are 380 but it is not divisible by 8. So, 94,380 is not divisible by 8.

A number is divisible by 9, if the sum of the digits of the number is divisible by 9.

The sum of the digits of the number 94,380 is 24 which is not divisible by 9.

Therefore, 94,380 is not divisible by 9.

A number is divisible by 10, if the number ends in 0.

The last digit of 94,380 is 0.

Hence, it is divisible by 10.

Therefore by the divisibility test, the number 94,380 is divisible only by 2, 3, 4, 5, 6 and 10.