# Find if a Number is Divisible by 23

A brief tutorial which explains the Divisibility Rule for 23. Using this rule you could identify whether the given number is divisible by 23 without performing the division operation. As per the rule, multiply the last digit by 7 and add the result to the remaining number; or multiply the last two digits by 3 and add the result to the remaining number; repeat this rule over and over again as necessary; if the result is divisible by 23, then the original number is divisible by 23.

## Divisibility Rule for 23

##### Rule 1:

Add 7 times the last digit to the remaining leading truncated number. Repeat this rule over and over again as necessary. If the result is divisible by 23, then the original number is also divisible by 23.

##### Example 1:

Find if the number 17043 is divisible by 23.

##### Solution :

Applying the divisibility rule for 23,

###### Step 1:

Add 7 times the last digit to the remaining leading truncated numbers (i.e) 1704 + 7 x 3 = 1725

###### Step 2:

Repeat step 1 until the number becomes smaller to get easily divisible by 23 (i.e) 172 + 7 x 5 = 207

###### Step 3:

20 + 7 x 7 = 69

Now, it is clear that 69 is divisible by 23. Hence the original number 17043 is also divisible by 23.

##### Rule 2:

Check whether the number is divisible by 3. Add the result to the remaining number. Repeat this rule over and over again as necessary until the result is divisible by 23.

##### Example 2:

Find if the number 345 is divisible by 23.

##### Solution :
###### Step 1:

Divide the last two digits by 3 (i.e) 45 / 3 = 15

###### Step 2:

Adding the resultant value to the remaining numbers, we get
15 + 3 = 18

###### Step 3:

Now, it is clear that 18 is divisible by 3 (i.e) 3 x 6 = 18

Hence, the original number 345 is also divisible by 23