Divisibility Test of 9

Define divisibility test

The test of divisibility is the procedure of determining if a particular number is precisely divisible by some other value without actually completing the division operations. Being absolutely divisible indicates that there can’t be any remainder after division.

Divisibility of 16:

The divisibility rule of 9 asserts that when a number’s total of all digits is divisible by 9, the said value is divisible by 9 as well. It supports us with a variety of topics namely HCF, LCM, measuring, and divisions. Divisibility through 9 seems to be a technique which enables us to determine whether or not a value is divisible by 9 without having to do lengthy division.

If you observe these numbers like 18, 45, 9, 27, 33, 36 and so on, you’ll be able to find a similarity between these given values, that is the sum of the digits of the number form a number that is divisible by 9. So, it shows that each of these numbers are multiples of 9 and the divisibility rule of 9 is satisfied.

Rule for larger numbers

The rule applies to huge numbers as well. The only change is that we repeat the divisibility check of 9 till the total digits of the number gets nearer 9 which will make it easy to compare or calculate a multiple from.

Let’s take an example value 365163. This number goes through the usual divisibility of 9 tests, that is, sum of all the digits. So, 3+6+5+1+6+3 = 24. We do the same with the new number 24 that is 2+4 = 6. The new resultant number 6 which isn’t divisible by 9, so the initial number isn’t divisible by 9.

Examples regarding divisibility by 16:

Example one:

Verify whether the number 8699 is divisible by 9.

Answer:

Add the digits in the number 8699 together.

8+6+9+9 = 32

The provided value 8699 has a total of its digits as 32 which isn’t divisible by 9.

As a result, 8699 isn’t divisible by nine.

Example two:

Check if the number 62622 is divisible by 9.

Answer:

After adding all the digits in the number 62622 together.

6+2+6+2+2 = 18

The resultant value from the calculation of the number has a total of its digits as 18 which is divisible by 9.

So after going through the divisibility test, the number 62622 is divisible by 9.

Example three:

Examine if the number 971352 is divisible by 9.

Answer:

After adding all the digits in the number 971352 together.

9+7+1+3+5+2 = 27

The output value by calculating all the digits of the given number is  27 which is divisible by 9.

So after going through the divisibility test, the number 971352 is divisible by 9.

Example four:

Verify if the number 4513 is divisible by 9.

Answer:

Add the digits in the number 4513 together.

4+5+1+3 = 13

The provided value 4513 has a total of its digits as 13 which isn’t divisible by 9.

As a result, 4513 isn’t divisible by nine.

Example 5:

Check if the number 56123 is divisible by 9.

Answer:

After adding all the digits in the number 56123 together.

5+6+1+2+3 = 17

The resultant value from the calculation of the number has a total of its digits as 17 which isn’t divisible by 9.

So following through the divisibility procedure, the number 56123 isn’t divisible by 9.

Conclusion:

This article takes the readers through the divisibility test and talks about how the divisibility rules work in case of divisibility test of 9. The article gives us unique examples regarding the divisibility process and mentions efficient and speedy ways for calculating the divisibility test of 9.