Divisibility Rules and Tests for CUET UG GAT – Concepts, Tricks, Formulas, and MCQs with Solutions

Introduction to Divisibility Rules and Tests

Divisibility Rules and Tests for CUET UG GAT  are important concepts in the Number System that help students quickly determine whether a number is divisible by another number without performing long division.

In CUET UG GAT , questions from divisibility rules frequently appear in:

• Number System
• Simplification
• LCM and HCF
• Arithmetic Reasoning
• Quantitative Aptitude

Mastering divisibility rules improves:

• Calculation speed
• Accuracy
• Time management
• Problem-solving efficiency

That is why this topic is considered a high-scoring and time-saving area in the CUET exam.

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What are Divisibility Rules and Tests?

Divisibility Rules are mathematical shortcuts used to check whether one number can be divided exactly by another number.

If a number can be divided completely without leaving a remainder, it is said to be divisible by that number.

Example:

24 ÷ 6 = 4

So, 24 is divisible by 6

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Important Divisibility Rules (Quick Revision)

Divisibility Rule of 2

A number is divisible by 2 if its last digit is even.

Examples:
12, 48, 90

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Divisibility Rule of 3

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

Example:
123

1 + 2 + 3 = 6

6 is divisible by 3

So, 123 is divisible by 3

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Divisibility Rule of 4

A number is divisible by 4 if the last two digits are divisible by 4.

Example:

316

Last two digits = 16

16 ÷ 4 = 4

So, divisible by 4

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Divisibility Rule of 5

A number is divisible by 5 if the last digit is:

0 or 5

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Divisibility Rule of 6

A number is divisible by 6 if:

• divisible by 2
  AND
• divisible by 3

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Divisibility Rule of 8

A number is divisible by 8 if the last three digits are divisible by 8.

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Divisibility Rule of 9

A number is divisible by 9 if the sum of digits is divisible by 9.

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Divisibility Rule of 10

A number is divisible by 10 if the last digit is 0.

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Divisibility Rule of 11

Difference between sum of alternate digits must be divisible by 11.

Example:

121

(1 + 1) − 2

= 0

So divisible by 11

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Why Divisibility Rules and Tests are Important for CUET UG GAT

This topic is important because:

1. Frequently asked in CUET exam
2. Helps solve questions quickly
3. Improves calculation speed
4. Saves time in exam
5. Forms base for many other topics
6. High scoring and easy marks topic

Expected Questions:

2 to 3 questions in CUET GAT

Difficulty Level:

Easy to Moderate

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Short Tricks to Solve Divisibility Questions

Trick 1

If a number is divisible by:

2 and 3

Then it is divisible by:

6

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Trick 2

If a number is divisible by:

3 and 4

Then it is divisible by:

12

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Trick 3

Remove zeros first.

Example:

1200

Ignore zeros

12

Check divisibility easily

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Trick 4

Use digit sum method for:

3 and 9

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Common Patterns of Questions in CUET

Most questions are based on:

• Finding smallest number divisible by
• Finding remainder
• Finding missing digit
• Checking divisibility
• Number formation
• LCM and HCF link questions

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Important Exam-Oriented  MCQs on Divisibility Rules and Tests for CUET UG GAT

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Q 4560) The smallest number which must be added to 5689 so that it becomes divisible by 9 is:

A. 5
B. 6
C. 7
D. 8

Answer

D. 4

Step-by-Step Solution

Sum of digits:

5 + 6 + 8 + 9 = 28

Next multiple of 9 after 28:

36

36 − 28 = 8

But we need remainder to become 0.

28 ÷ 9 leaves remainder:

1

So, the smallest number which must be added:

9 − 1 = 8

Q 4561) The smallest number divisible by 5 and 6 is:

A. 20
B. 25
C. 30
D. 35

Answer

C. 30

Solution

LCM:

5 = 5
6 = 2 × 3

LCM:

2 × 3 × 5

= 30

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Q 4562) Find the smallest number to be subtracted from 7316 so that it becomes divisible by 4.

A. 1
B. 0
C. 2
D. 3

Answer

B. 0

Solution

Last two digit:

16

 Divisible by 4.

Subtract:

0

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Q 4563) Which of the following numbers is divisible by 11?

A. 2732
B. 2735
C. 2728
D. 2756

Answer

C. 2728

Solution

Odd positions:

2 + 2 = 4

Even positions:

7 + 8 = 15

Difference:

15 − 4 = 11

Divisible by 11.

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Q 4564) A number when divided by 9 leaves remainder 6. What must be added to make it divisible by 9?

A. 1
B. 2
C. 3
D. 4

Answer

C. 3

Solution

To make divisible:

Add:

9 − 6 = 3

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Q 4565) The greatest 4 digit number divisible by 3 is:

A. 9996
B. 9997
C. 9998
D. 9999

Answer

D. 9999

Solution

Digit sum:

9 + 9 + 9 + 9 = 36

36 divisible by 3

Q 4566) Which number is divisible by 9?

A. 1456
B. 1458
C. 1459
D. 1460

Answer

B. 1458

Solution

Digit sum:

1 + 4 + 5 + 8 = 18

Divisible by 9.

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Q 4567) A number leaves remainder 5 when divided by 8. What must be added to make it divisible by 8?

A. 9
B. 7
C. 5
D. 3

Answer

D. 3

Solution

Add:

8 − 5 = 3

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Q 4568) The smallest 3-digit number divisible by 7 is:

A. 117
B. 109
C. 105
D. 100

Answer

C. 105

Solution

Smallest 3-digit number:

100

Next multiple of 7:

105

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Q 4569) Which of the following numbers is divisible by 4?

A. 468
B. 472
C. 476
D. 479

Answer

A. 468

Solution

Last two digits:

68

68 ÷ 4 = 17

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FAQs on Divisibility Rules and Tests

Q1. What are divisibility rules?

Divisibility rules are shortcuts used to check whether a number can be divided exactly by another number.

Q2. How many questions come from divisibility rules in CUET?

Usually:

2 to 3 questions

Q3. Is divisibility rules topic easy?

Yes.
It is considered one of the easiest and most scoring topics in CUET maths.

Q4. Is divisibility rules important for other exams?

Yes.

Important for:

CUET
SSC
Banking
Railway
Defence exams

Internal Linking

Number System Mock Test for CUET UG GAT 2026: MCQs with Answers (CUET Pattern)

Factors and Multiples for CUET UG GAT 2026: Concepts, Tricks, Formulas, and MCQs with Solutions

LCM and HCF for CUET UG GAT 2026 – Formulas, Tricks, Questions, and Solutions

 

Conclusion

Divisibility Rules and Tests is one of the most important and easiest topics in the Number System for CUET UG GAT. By learning simple rules and shortcuts, students can quickly identify divisible numbers, save time, and improve accuracy in exams.

Practicing MCQs regularly and understanding patterns will help students score high marks with minimal effort.

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