Divisibility Rules for Class 6: A Complete Guide with Solved Examples

Divisibility rules are simple shortcuts that help quickly determine whether one number can be divided by another without performing long division. These rules are especially useful for students as they build a strong foundation in number sense and make calculations faster and more accurate. In this chapter, you’ll learn easy tricks to check divisibility from 1 to 13 using clear examples and step-by-step methods.

Table of Contents

• What are Divisibility Rules?
• Properties of Divisibility
• Divisibility Rules from 1 to 13
• Solved Example on Divisibility Rules for Class 6
• Practice Questions on Divisibility Rules for Class 6

What are Divisibility Rules?

A divisibility rule is a quick test that tells you whether a number can be divided by another number without leaving a remainder. In other words, if a number is ‘divisible’ by another, the result of the division is a whole number with nothing left over.

For example:

• 18 ÷ 3 = 6; No remainder, so 18 is divisible by 3. 

• 20 ÷ 3 = 6.66... ; There's a remainder, so 20 is not divisible by 3. 

Instead of doing that division every time, divisibility rules give you a shortcut.

Properties of Divisibility

1. Divisibility of sum of numbers: If a number is divisible by a given number, then their sum is also divisible by that number.
   Example: 7 divides 28 and 35. Therefore, 63 = 28 + 35 is also divisible by 7.

2. Divisibility by the difference of the numbers: If any number is divisible by a given number, then their difference is also divisible by the same number.
   Example: 4 divides 28 and 40. Therefore, 12 = 40 - 28 is also divisible by 4.

3. Divisibility by factors: If any number is divisible by another number, then the number is also divisible by its factors.
   Example: 24 is divisible by 6. It means 24 is also divisible by the factors of 6. i.e., 24 is divisible by 2 and 3 as well.

4. Divisibility by product of co-primes: If any number is divisible by two or more co-primes, then it is always divisible by the product of the co-primes.
   Example: 30 is divisible by the co-prime numbers 2, 3 and 5. Therefore, 30 is also divisible by 6 = 2 × 3, 15 = 3 × 5 and 10 = 2 × 5

Divisibility Rules from 1 to 13

• Divisibility Rule of 1:
  Every integer is divisible by 1.
  Any whole number divided by 1 gives that number itself. 5 ÷ 1 = 5. 1,000,000 ÷ 1 = 1,000,000. Always.

• Divisibility Rule of 2:
  Rule: A number is divisible by 2 if its last digit is even, that is, if it ends in 0, 2, 4, 6, or 8. Only the last digit matters when dividing by 2, because all higher place values (tens, hundreds, thousands) are already multiples of 2.
  Examples:

• • 348: ends in 8 ⇒  Divisible by 2

  • 7,210: ends in 0 ⇒ Divisible by 2

  • 4,563: ends in 3 ⇒  Not divisible by 2
    If it ends in an odd digit (1, 3, 5, 7, 9), it's odd and therefore not divisible by 2.

• Divisibility Rule of 3:
  Rule: A number is divisible by 3 if the sum of its digits is divisible by 3.
  Add up all the digits and check the result.
  Examples:

• • 561: 5 + 6 + 1 = 12; 12 ÷ 3 = 4 ⇒  561 is divisible by 3

  • 7,452: 7 + 4 + 5 + 2 = 18; 18 ÷ 3 = 6 ⇒ 7,452 is divisible by 3

  • 844: 8 + 4 + 4 = 16; 16 ÷ 3 = 5.33… ⇒ 844 is not divisible by 3
    If your digit sum is still large, keep adding until you get a single or two-digit number. For 99,996: 9 + 9 + 9 + 9 + 6 = 42. ⇒ 4 + 2 = 6 ⇒ divisible by 3

• Divisibility Rule of 4:
  Rule: A number is divisible by 4 if its last two digits form a number divisible by 4.
  Why the last two digits? Because 100 is divisible by 4 (100 ÷ 4 = 25), so any hundreds, thousands, and higher values are already taken care of. Only the last two digits determine divisibility by 4.
  Examples:

• • 1,312:  last two digits: 12 → 12 ÷ 4 = 3 ⇒ Divisible by 4

  • 45,836: last two digits: 36 → 36 ÷ 4 = 9 ⇒  Divisible by 4

  • 7,018: last two digits: 18 → 18 ÷ 4 = 4.5 ⇒ Not divisible by 4

• Divisibility Rule of 5:
  Rule: A number is divisible by 5 if its last digit is 0 or 5.
  Counting by 5s always ends in 5 or 0.
  Examples:

• • 785: ends in 5 ⇒  Divisible by 5

  • 3,400: ends in 0 ⇒  Divisible by 5

  • 2,763: ends in 3 ⇒  Not divisible by 5

• Divisibility Rule of 6:
  Rule: A number is divisible by 6 if it is divisible by both 2 and 3.
  Since 6 = 2 × 3, and 2 and 3 share no common factors, a number must satisfy both the rule of 2 and the rule of 3.
  Examples:

• • 414:  ends in 4 (divisible by 2); 4+1+4 = 9 (divisible by 3) ⇒  Divisible by 6.

  • 308: ends in 8 (divisible by 2);  3+0+8 = 11 (not divisible by 3) ⇒ Not divisible by 6 

  • 135: ends in 5 (not divisible by 2) ⇒  Not divisible by 6

• Divisibility Rule of 7:
  Rule: Take the last digit, double it, and subtract from the remaining number. If the result is 0 or divisible by 7, the original number is divisible by 7. Repeat the process if the result is still large.
  Example 1: Is 672 divisible by 7?
  Last digit: 2. Double it: 4
  Remaining number: 67
  67 − 4 = 63
  63 ÷ 7 = 9 ⇒ Divisible by 7
  Example 2: Is 905 divisible by 7?
  Last digit: 5; Double it: 10
  Remaining number: 90
  90 − 10 = 80
  80 ÷ 7 = 11.4... ⇒  Not divisible by 7

• Divisibility Rule of 8:
  Rule: A number is divisible by 8 if its last three digits are divisible by 8.
  Since 1,000 = 8 × 125, everything from the thousands place upward is already a multiple of 8. So only the last three digits matter.
  Examples:

• • 5,832: last three digits: 832 → 832 ÷ 8 = 104 ⇒ Divisible by 8

  • 3,126: last three digits: 126 → 126 ÷ 8 = 15.75 ⇒ Not divisible by 8

• Divisibility Rule of 9:
  Rule: A number is divisible by 9 if the sum of its digits is divisible by 9.
  Examples:

• • 4,725: 4+7+2+5 = 18 → 18 ÷ 9 = 2  ⇒ Divisible by 9

  • 90,453: 9+0+4+5+3 = 21 → 21 ÷ 9 = 2.33...  ⇒  Not divisible by 9

• Divisibility Rule of 10:
  Rule: A number is divisible by 10 if its last digit is 0.
  Every multiple of 10 ends in zero: 10, 20, 30, 100, 250, 1,000…

• Divisibility Rule of 11:
  Rule: Alternately add and subtract the digits from left to right. If the result is 0 or divisible by 11, the number is divisible by 11.
  Starting from the leftmost digit, assign alternating + and − signs: add the 1st digit, subtract the 2nd, add the 3rd, subtract the 4th, and so on.
  Examples:

• • 1,364: +1 − 3 + 6 − 4 = 0; 0 is divisible by 11 

  • 91,828: +9 − 1 + 8 − 2 + 8 = 22 → 22 ÷ 11 = 2 ⇒ Divisible by 11

  • 987: +9 − 8 + 7 = 8 ⇒ not divisible by 11 

• Divisibility Rule of 12:
  Rule: A number is divisible by 12 if it is divisible by both 3 and 4.
  Since 12 = 3 × 4, and 3 and 4 share no common factors, simply apply both rules.
  Example: Is 3,276 divisible by 12?
  Check for 3: 3+2+7+6 = 18; 18 ÷ 3 = 6
  Check for 4: Last two digits are 76; 76 ÷ 4 = 19
  ⇒ 3,276 is divisible by 12 

• Divisibility Rule of 13:
  Rule: Multiply the last digit by 4 and add it to the rest of the number. Repeat until you reach a two-digit number. If the result is divisible by 13, the original number is.
  Example: Is 546 divisible by 13?
  Last digit is 6, 6 × 4 = 24
  54 + 24 = 78
  78 ÷ 13 = 6 ⇒ Divisible by 13

Solved Example on Divisibility Rules for Class 6

Example 1: Check if 246 is divisible by 2.

Solution: A number is divisible by 2 if its last digit is even. 246 ends in 6 (even), so it is divisible by 2.

Example 2: Check if 3,465 is divisible by 9.

Solution: Add the digits: 3 + 4 + 6 + 5 = 18. Since 18 is divisible by 9, 3,465 is divisible by 9.

Example 3: Check if 1,248 is divisible by 4.

Solution: The last two digits are 48. Since 48 is divisible by 4, 1,248 is divisible by 4.

Example 4: Is 735 divisible by 3?

Solution: Add the digits: 7 + 3 + 5 = 15. Since 15 is divisible by 3, 735 is divisible by 3.

Example 5: Is 3751 divisible by 11?

Solution: Take the alternating sum: (3 + 5) − (7 + 1) = 8 − 8 = 0

Since the result is 0, 3751 is divisible by 11.

Practice Questions on Divisibility Rules for Class 6

1. Is 4,536 divisible by 3?

2. Is 7,128 divisible by 8?

3. Is 45,034 divisible by 11?

4. Is 2,310 divisible by 6?

5. Is 8,463 divisible by 9?

6. Is 7,450 divisible by 5?

7. Check if 2,574 is divisible by 11.

8. Check whether 6,372 is divisible by 6.

9. Check whether 468 is divisible by 2.

10. Is 2,366 divisible by 13?