Divisibility Rules for JNV Entrance Test 2025

Divisibility rules are essential tools that help quickly determine if a number is divisible by another without performing the actual division. These rules are commonly tested in competitive exams, including the JNV Entrance Test. Understanding these rules will help you solve problems more efficiently.

This section will cover the divisibility rules for all numbers from 1 to 10, along with examples to help you understand their applications.

1. Divisibility Rule for 1

Rule: Every number is divisible by 1.
Explanation: Any integer is divisible by 1. This is the simplest divisibility rule because all numbers have 1 as a divisor.
Example:
- 25 ÷ 1 = 25 (Divisible)
- 1023 ÷ 1 = 1023 (Divisible)

2. Divisibility Rule for 2

Rule: A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.
Explanation: If the number ends in an even digit, it is divisible by 2.
Example:
- 246 (ends in 6, which is even) → Divisible by 2.
- 145 (ends in 5, which is odd) → Not divisible by 2.

3. Divisibility Rule for 3

Rule: A number is divisible by 3 if the sum of its digits is divisible by 3.
Explanation: Add all the digits of the number and check if the result is divisible by 3.
Example:
- 123: The sum of digits = 1 + 2 + 3 = 6 → 6 is divisible by 3 → 123 is divisible by 3.
- 145: The sum of digits = 1 + 4 + 5 = 10 → 10 is not divisible by 3 → 145 is not divisible by 3.

4. Divisibility Rule for 4

Rule: A number is divisible by 4 if the last two digits of the number form a number divisible by 4.
Explanation: Check if the number formed by the last two digits is divisible by 4.
Example:
- 316: The last two digits are 16 → 16 is divisible by 4 → 316 is divisible by 4.
- 123: The last two digits are 23 → 23 is not divisible by 4 → 123 is not divisible by 4.

5. Divisibility Rule for 5

Rule: A number is divisible by 5 if its last digit is either 0 or 5.
Explanation: If the number ends in 0 or 5, it is divisible by 5.
Example:
- 150 (ends in 0) → Divisible by 5.
- 287 (ends in 7) → Not divisible by 5.
- 55 (ends in 5) → Divisible by 5.

6. Divisibility Rule for 6

Rule: A number is divisible by 6 if it is divisible by both 2 and 3.
Explanation: The number must satisfy both the divisibility rules for 2 and 3.
Example:
- 12: Ends in 2 (divisible by 2), and the sum of digits is 1 + 2 = 3 (divisible by 3) → 12 is divisible by 6.
- 15: Ends in 5 (not divisible by 2), and the sum of digits is 1 + 5 = 6 (divisible by 3) → 15 is not divisible by 6.

7. Divisibility Rule for 7

Rule: To check if a number is divisible by 7, you can double the last digit, subtract it from the rest of the number, and check if the result is divisible by 7.
Explanation: Perform the subtraction of double the last digit and check if the remaining number is divisible by 7.
Example:
- 63: Double the last digit (3 × 2 = 6), subtract it from the remaining part (6 - 6 = 0), and 0 is divisible by 7 → 63 is divisible by 7.
- 42: Double the last digit (2 × 2 = 4), subtract it from the remaining part (4 - 4 = 0), and 0 is divisible by 7 → 42 is divisible by 7.
- 58: Double the last digit (8 × 2 = 16), subtract it from the remaining part (5 - 16 = -11), and -11 is not divisible by 7 → 58 is not divisible by 7.

8. Divisibility Rule for 8

Rule: A number is divisible by 8 if the last three digits of the number form a number divisible by 8.
Explanation: Check if the number formed by the last three digits is divisible by 8.
Example:
- 1128: The last three digits are 128 → 128 ÷ 8 = 16 → 1128 is divisible by 8.
- 230: The last three digits are 230 → 230 ÷ 8 = 28.75 → 230 is not divisible by 8.

9. Divisibility Rule for 9

Rule: A number is divisible by 9 if the sum of its digits is divisible by 9.
Explanation: Add all the digits of the number and check if the sum is divisible by 9.
Example:
- 45: The sum of digits = 4 + 5 = 9 → 9 is divisible by 9 → 45 is divisible by 9.
- 1224: The sum of digits = 1 + 2 + 2 + 4 = 9 → 9 is divisible by 9 → 1224 is divisible by 9.
- 987: The sum of digits = 9 + 8 + 7 = 24 → 24 is not divisible by 9 → 987 is not divisible by 9.

10. Divisibility Rule for 10

Rule: A number is divisible by 10 if its last digit is 0.
Explanation: If the number ends in 0, it is divisible by 10.
Example:
- 30 (ends in 0) → Divisible by 10.
- 105 (ends in 5) → Not divisible by 10.
- 550 (ends in 0) → Divisible by 10.

11. Divisibility Rule for 11

Rule: A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is divisible by 11.
Explanation: Subtract the sum of digits in even positions from the sum of digits in odd positions. If the result is divisible by 11, then the number is divisible by 11.
Example:
- 2728: The sum of digits in odd positions = 2 + 2 = 4, and the sum of digits in even positions = 7 + 8 = 15. The difference is 15 - 4 = 11, which is divisible by 11 → 2728 is divisible by 11.
- 1234: The sum of digits in odd positions = 1 + 3 = 4, and the sum of digits in even positions = 2 + 4 = 6. The difference is 6 - 4 = 2, which is not divisible by 11 → 1234 is not divisible by 11.

Conclusion

Mastering the divisibility rules is an important skill for the JNV Entrance Test 2025. These rules help solve problems involving divisibility quickly without performing long divisions. Understanding and practicing these rules can give you an advantage in answering questions more efficiently and accurately.

By following the explanations and examples for each rule, you can confidently apply them in your test preparation. With consistent practice, you’ll be able to handle divisibility questions swiftly and effectively.

Jawahar Navodaya Vidyalaya Samiti (JNVS) Entrance Exams