Last updated on May 26th, 2025
The divisibility rule is a way to find out whether a number is divisible by another number without using the division method. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting things. In this topic, we will learn about the 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.
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.
The divisibility rule of 21 helps us to quickly check if the given number is divisible by 21, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes that will help you to understand.
Is 189 divisible by 21?
Yes, 189 is divisible by 21.
To determine if 189 is divisible by 21, we can apply the divisibility rules for both 3 and 7.
1) Check divisibility by 3: Add the digits, 1 + 8 + 9 = 18. Since 18 is divisible by 3, 189 passes this test.
2) Check divisibility by 7: Multiply the last digit by 2, 9 × 2 = 18. Subtract from the remaining digits, 18 - 18 = 0. Since 0 is a multiple of 7, 189 also passes this test.
Since 189 is divisible by both 3 and 7, it is divisible by 21.
Check the divisibility rule of 21 for 252.
Yes, 252 is divisible by 21.
To check if 252 is divisible by 21, we use the divisibility rules for 3 and 7.
1) Divisibility by 3: Add the digits, 2 + 5 + 2 = 9. Since 9 is divisible by 3, 252 passes this test.
2) Divisibility by 7: Multiply the last digit by 2, 2 × 2 = 4. Subtract from the remaining digits, 25 - 4 = 21. Since 21 is a multiple of 7, 252 passes this test.
Therefore, 252 is divisible by 21.
Is 63 divisible by 21?
Yes, 63 is divisible by 21.
To verify if 63 is divisible by 21, we need to check its divisibility by both 3 and 7.
1) Divisibility by 3: Add the digits, 6 + 3 = 9. Since 9 is divisible by 3, 63 passes this test.
2) Divisibility by 7: Multiply the last digit by 2, 3 × 2 = 6. Subtract from the remaining digits, 6 - 6 = 0. Since 0 is a multiple of 7, 63 passes this test.
Thus, 63 is divisible by 21.
Can 154 be divisible by 21 following the divisibility rule?
No, 154 is not divisible by 21.
To check if 154 is divisible by 21, apply the divisibility rules for 3 and 7.
1) Divisibility by 3: Add the digits, 1 + 5 + 4 = 10. Since 10 is not divisible by 3, 154 fails this test.
2) Divisibility by 7: Multiply the last digit by 2, 4 × 2 = 8. Subtract from the remaining digits, 15 - 8 = 7. Since 7 is a multiple of 7, 154 passes this test.
Since 154 is not divisible by 3, it is not divisible by 21.
Check the divisibility rule of 21 for 441.
Yes, 441 is divisible by 21.
To determine if 441 is divisible by 21, we use the divisibility rules for 3 and 7.
1) Divisibility by 3: Add the digits, 4 + 4 + 1 = 9. Since 9 is divisible by 3, 441 passes this test.
2) Divisibility by 7: Multiply the last digit by 2, 1 × 2 = 2. Subtract from the remaining digits, 44 - 2 = 42. Since 42 is a multiple of 7, 441 passes this test.
Therefore, 441 is divisible by 21.
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.