Question

Test the divisibility of the following number by 9: 2358

Answer 1

Hint: We solve this question by using the tests of divisibility for the given number. We are required to find if the number 2358 is divisible by 9 by using the divisibility rule for the division by 9. The divisibility by 9 rule states that the sum of digits of the number should be a multiple of 9 in order for the number to be divisible by 9.

Complete step by step answer:
In order to solve this question, let us first state the divisibility rule for a number to be divisible by 9. For a number to be divisible by 9, the sum of digits of the number should be a multiple of 9 or divisible by 9. Given number is 2358. Let us calculate the sum of the digits for this number. Adding up all the digits of the number,
$\Rightarrow 2+3+5+8=18$
Hence, the sum of the digits obtained by adding all the digits of the number 2358 is 18. We know that 18 is divisible by 9. Dividing the two numbers gives us 2. Since the sum of the digits of 2358 is divisible by 9, then the number 2358 itself is divisible by 9.
Hence, the number 2358 is divisible by 9.

Note: We need to know the test of divisibility for 9 in order to solve such sums. By knowing these rules, we do not need to actually divide the number to say if it is divisible by a particular number or not. By just using the tests of divisibility, we can tell if a number is divisible by the given number or not.