Find if a Number is Divisible by 21


A brief tutorial which explains the divisibility rule for 21. Using this rule you could identify whether the given number is divisible by 21. As per the rule, multiply the last digit by 2 and subtract the result from the remaining number and continue until the result gets single digit. If the result is 0, the number is divisible by 21. Or, if the original number is divisible by 3 and 7, it is divisible by 21.

Divisibility Rule for 21

Rule 1:

Subtract twice the last digit from the remaining numbers. Apply this rule over and over again as necessary.

Example

Find if the number 18753 is divisible by 21.

Solution :

Applying the divisibility rule for 21,

Step 1:

Consider the last digit (i.e) 3 Subtract twice the digit from the remaining numbers (i.e)1875 – 3 – 3 = 1869

Step 2:

Repeat the same steps as step 1 until the resultant value becomes 0 186 – 9 – 9 = 168

Step 3:

16 – 8 – 8 = 0

Here, the original number 18753 is divisible by 21, hence the final number is 0.

Rule 2:

If the given number is divisible by 3 & 7, then the original number is also divisible by 21.

Example 2:

Find if the number 168 is divisible by 21. Applying the divisibility rule for 21,

Step 1:

Check whether the given number 168 is divisible by 3 3 x 56 = 168 Hence, the number 168 is divisible by 3.

Step 2:

Check whether the given number 168 is divisible by 7 7 x 24 = 168 Hence, the number 168 is divisible by 7.

Step 3:

Since the number 168 is divisible by both 7 and 3, it is also divisible by 21.

Note:

Keep repeating this procedure until a number less than 21 is obtained.
A number is divisible by 21 if and only if the final number is 0.


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