Divisibility Rule of 21

The divisibility rule for 21 is a method by which we can find out if a number is divisible by 21 without using the division method. Check whether 462 is divisible by 21 with the divisibility rule.  

Step 1: Check if the number is divisible by 3. Add up all the digits in the number and see if the sum is divisible by 3. For 462, the sum of digits is 4+6+2=12, which is divisible by 3.

Step 2: Check if the number is divisible by 7. Use the divisibility rule of 7: double the last digit and subtract it from the rest of the number. For 462, double the last digit: 2×2=4. Subtract from the rest: 46-4=42, which is divisible by 7.

Step 3: Since the number is divisible by both 3 and 7, it is divisible by 21.

Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 21.

• Know the multiples of 21: Memorize the multiples of 21 (21, 42, 63, 84… etc.) to quickly check divisibility. If the result from any divisibility test is a multiple of 21, then the number is divisible by 21.

• Use the divisibility rules for both 3 and 7: A number must satisfy both the rule for 3 and the rule for 7 to be divisible by 21.

• Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that can be easily evaluated. For example, check if 882 is divisible by 21 using the divisibility test. 
   

           For 3: The sum of digits is 8+8+2=18, which is divisible by 3.
           For 7: Double the last digit, 2×2=4. Subtract from the rest, 88 - 4 = 84, which is divisible by 7.
           Hence, 882 is divisible by 21.
 

• Use the division method to verify: Students can use the division method as a way to verify and cross-check their results. This will help them to verify and also learn.

• Divisibility Rule: A set of guidelines used to determine whether a number is divisible by another number without performing division.

• Multiples: The result of multiplying a number by an integer. For example, multiples of 21 are 21, 42, 63, etc.

• Integers: The set of whole numbers and their opposites, including positive numbers, negative numbers, and zero.

• Subtraction: A mathematical operation that involves removing one number from another to find the difference.

• Sum: The result of adding two or more numbers together.