Divisibility Rules above Number 19

Divisibility rules help you quickly check if a number can be divided by another number without doing the full division. Imagine a student has 1,244 candies and needs to share them equally among 23 friends. Instead of dividing 1,244 by 23 directly, he can use the divisibility rule for 23 to check whether he can distribute the candies equally.

These rules provide simple steps, saving time and effort in determining divisibility for larger numbers.

Table for the Divisibility Rules for 20 to 30

Read More about Divisibility Rules from 1 to 19.

Divisibility Rule of 20

A number is divisible by 20 if the last two digits of the number form a number that is divisible by 20. The valid last two digits for divisibility by 20 are 00, 20, 40, 60, and 80.

Example: 2580, 4560, and 90020 are divisible by 20.

Divisibility Rule of 21

A number is divisible by 21 if it meets the following conditions:

• Divisible by 3: the sum of the digits of the number must be divisible by 3.
• Divisible by 7: Subtract twice the last digit from the rest of the number and check if the result is divisible by 7.

Example: Determine if 147 is divisible by 21.

• Check for Divisibility by 3: 1 + 4 + 7 = 12 (12 is divisible by 3).
• Check for Divisibility by 7: Take the last digit (7), double it (14), and subtract it from the rest (14 - 14 = 0). Since 0 is divisible by 7, 147 is divisible by 7.

Therefore, 147 is divisible by 21.

Divisibility Rule of 22

A number is divisible by 22 if it meets the following conditions:

• Divisible by 2: The last digit of the number must be even
• Divisible by 11: Subtract the sum of the digits in the odd positions from the sum of the digits in the even positions, and check if the result is divisible by 11.

Example: Verify whether 484 can be divided evenly by 22.

• Check for Divisibility by 2: The last digit is 4, which is even, so 484 is divisible by 2.
• Check for Divisibility by 11:
  • Odd positions: 4 + 4 = 8 (first and third digits).
  • Even positions: 8 (second digit).
  • Difference: 8 − 8 = 0 (0 is divisible by 11).
  • Therefore, 484 is divisible by 11.

Since 484 is divisible by both 2 and 11, it is also divisible by 22.

Divisibility Rule of 23

A number is divisible by 23 if the result is obtained by multiplying the last digit by 7 and adding it to is the rest of the number, it is divisible by 23.

Example: Check if 529 divides perfectly by 23.

• Last digit: 9
• Multiply by 7: 9 × 7 = 63
• Add to the rest: 52 + 63 = 115

Now check if 115 is divisible by 23:

• 115 ÷ 23 = 5

Therefore, 529 is divisible by 23.

Divisibility Rule for 24

A number is divisible by 24 if it meets the following conditions:

• Divisible by 3: The sum of the digits of the number must be divisible by 3.
• Divisible by 8: The last three digits of the number must form a number that is divisible by 8.

Example: Find out if 3,072 is fully divisible by 24.

• Check for divisibility by 3:
  • Sum of digits: 3 + 0 + 7 + 2 = 12
  • Since 12 ÷ 3 = 4, it is divisible by 3.
• Check for divisibility by 8:
  • Last three digits: 072 (or just 72)
  • 72 ÷ 8 = 9, so it is divisible by 8.

Thus, 3,072 is also divisible by 24.

Divisibility Rule for 25

A number is divisible by 25 if its last two digits form a number that is divisible by 25. Specifically, the last two digits must be 00, 25, 50, or 75.

Example: Check if 3,150 divides perfectly by 25.

• Last two digits: 50

Since 50 is divisible by 25, the number 3,150 is divisible by 25.

Divisibility Rule for 26

A number is divisible by 26 if it meets the following conditions:

• Divisible by 2: The last digit of the number must be even (i.e., it should be 0, 2, 4, 6, or 8).
• Divisible by 13: The number itself must also be divisible by 13.

Example: Find out if 1300 is fully divisible by 26.

• Check for divisibility by 2:
  • Last digit: 0 (even)
  • It satisfies the condition for 2.
• Check for divisibility by 13:
  • 1300 ÷ 13 = 100, so it is divisible by 13.

Thus, 1300 is also divisible by 26.

Divisibility Rule of 27

Multiply the last digit of the number by 8, then subtract it from the rest of the number. The original number is divisible by 27 if and only if the final result is also divisible by 27.

Example: Check if 4,050 divides perfectly by 27.

• Last digit: 0
  • Multiply by 8: 0 × 8 = 0
• Subtract from the rest:
  • Rest of the number: 405
  • Calculation: 405 − 0 = 405
• Again, follow the step 1 and step 2
  • Multiply the last digit by 8: 5 × 8 = 40
  • Subtract from the rest: 40 - 40 = 0

Since the final result 0 is divisible by 27, 4,050 is also divisible by 27.

Divisibility Rule of 28

A number is divisible by 28 if it meets the following conditions:

1. Divisible by 4:
   • The last two digits of the number must be divisible by 4.
2. Divisible by 7:
   • Subtract twice and the last digit from the rest of the number and check if the result is divisible by 7.

Example: Find out if 812 is fully divisible by 28.

1. Check divisibility by 4:
   • Last two digits: 12
   • 12 ÷ 4 (divisible by 4)
2. Check for Divisibility by 7: Take the last digit (2), double it (4), and subtract it from the rest (81 - 4 = 77). Since 77 is divisible by 7, 812 is divisible by 7

Since both conditions are met, 812 is divisible by 28.

Divisibility by 29

Add 3 times the last digit, and add this result to the rest of the number (the digits excluding the last one). The original number is divisible by 29 if and only if the resulting number is divisible by 29.

Example: Check if 551 divides perfectly by 29.

• Last digit: 1
  • Multiply by 3: 1 × 3 = 3
• Add to the rest of the number:
  • Rest of the number: 55
  • Calculation: 55 + 3 = 58
• Again, follow the step 1 and step 2
  • Multiply the last digit by 3: 8 × 3 = 24
  • Add to the rest of the number: 5 + 24 = 29

Since, the final result 29 is divisible by 29, 551 is also divisible by 29.

Divisibility Rule for 30

A number is divisible by 30 if it meets the following conditions:

• Divisible by 2: The last digit of the number must be even (0, 2, 4, 6, or 8).
• Divisible by 3: The sum of the digits must be divisible by 3.
• Divisible by 5: The last digit of the number must be either 0 or 5.

Example: Check to see if 150 divides evenly by 30.

• Divisible by 2: The last digit is 0 (even), so it is divisible by 2.
• Divisible by 3:
  • Sum of the digits: 1 + 5 + 0 = 6
  • Since 6 is divisible by 3, the number is also divisible by 3.
• Divisible by 5: The last digit is 0, so it is divisible by 5.

Since 150 meets all three conditions, it is divisible by 30.

Read More,

• Division
• Easy Division Tricks
• Top 30 Math Tricks for Fast Calculations
• Quiz about Number Divisibility

Examples on Divisibility Rules

Example 1: Use divisibility rules to check whether 2068965 is divisible by 23 

Solution:

Check 2068965 is divisible by 23 

• 2068965 ⇒ 206896 + 5 × 7 = 206931
• 206931 ⇒ 20693 + 1 × 7 = 20700
• 20700 ⇒ 2070 + 0 × 7 = 2070
• 2070 ⇒ 207 + 0 × 7 = 207
• 207 ⇒ 20+ 7 × 7 = 69

Since 69 is divisible by 23 (69/23 = 3)

2068965 is also divisible by 23.

Example 2: Check if 6,120 is divisible by 30.

Solution:

• A number is divisible by 30 if it is divisible by 2, 3, and 5.
• Check for 2: Last digit is 0 (even). Divisible by 2
• Check for 3: Sum of digits = 6 + 1 + 2 + 0 = 9
• Check for 5: Last digit is 0. Divisible by 5.
• Therefore, 6,120 is divisible by 30.

Example 3: check if 2,086,956 is divisible by 29.

Solution:

Check 2086956 is divisible by 29 

• 2086956 ⇒ 208695 + 6 × 3 = 208713
• 208713 ⇒ 20871 + 1 × 3 = 20880
• 20880 ⇒ 2088 + 0 × 3 = 2088
• 2088 ⇒ 208 + 8 × 3 = 232
• 232 ⇒ 23 + 2 × 3 = 29

Since 29 is divisible by 29

2086956 is also divisible by 29.