Divisibility Rule For 21 With Examples

Divisibility Rule For 21

The divisibility rule for 21 is based on the fact that (21 = 3 x 7). Therefore, to determine if a number is divisible by 21, it must satisfy the divisibility rules for both 3 and 7.

1. Divisibility Rule for 3:

A number is divisible by 3 if the sum of its digits is divisible by 3.

2. Divisibility Rule for 7:

The rule for 7 is a bit more complex:

• Take the last digit of the number.
• Double that last digit.
• Subtract the doubled value from the rest of the number.
• If the result is divisible by 7 (including 0), then the original number is divisible by 7.

Combining the Rules for 21:

For a number to be divisible by 21, it must:

• Be divisible by 3 (the sum of its digits is divisible by 3).
• Be divisible by 7 (using the method outlined above).

Examples:

1. Example: 126

• Divisibility by 3:
  • Sum of digits: (1 + 2 + 6 = 9) (which is divisible by 3).
• Divisibility by 7:
  • Last digit: 6
  • Double it: (6 x 2 = 12)
  • Subtract from the rest: (12 – 12 = 0) (which is divisible by 7).
• Both conditions are met, so 126 is divisible by 21.

1. Example: 147

• Divisibility by 3:
  • Sum of digits: (1 + 4 + 7 = 12) (which is divisible by 3).
• Divisibility by 7:
  • Last digit: 7
  • Double it: (7 x 2 = 14)
  • Subtract from the rest: (14 – 14 = 0) (which is divisible by 7).
• Both conditions are met, so 147 is divisible by 21.

1. Example: 175

• Divisibility by 3:
  • Sum of digits: (1 + 7 + 5 = 13) (not divisible by 3).
• Since it’s not divisible by 3, 175 is not divisible by 21.

1. Example: 84

• Divisibility by 3:
  • Sum of digits: (8 + 4 = 12) (which is divisible by 3).
• Divisibility by 7:
  • Last digit: 4
  • Double it: (4 x 2 = 8)
  • Subtract from the rest: (8 – 8 = 0) (which is divisible by 7).
• Both conditions are met, so 84 is divisible by 21.

1. Example: 100

• Divisibility by 3:
  • Sum of digits: (1 + 0 + 0 = 1) (not divisible by 3).
• Since it’s not divisible by 3, 100 is not divisible by 21.

Conclusion

To determine if a number is divisible by 21, check:

• If the sum of its digits is divisible by 3.
• If the number passes the subtraction method for 7.

Both conditions must be satisfied for the number to be divisible by 21.