Abhyank Srinet 
Table of Contents
- Introduction
- What Is GMAT Divisibility and Why Is It Tested?
- Which GMAT Divisibility Rules Should You Memorise?
- How Do Composite Divisibility Rules Work?
- How Do You Use Divisibility for Factors and Prime Numbers?
- How Are GMAT Divisibility and Remainders Connected?
- How Can You Solve GMAT Divisibility Questions Faster?
- Which GMAT Divisibility Mistakes Should You Avoid?
- How Do You Practise GMAT Divisibility Questions?
- Which Official Resources Should You Use for GMAT Practice?
- How Should Indian Applicants Prepare GMAT Divisibility?
GMAT divisibility rules help you determine whether one integer divides another without leaving a remainder. The most important rules to learn are for 2, 3, 4, 5, 6, 8, 9, 10, 11 and 12. These shortcuts help solve questions involving factors, multiples, prime numbers and remainders without lengthy division.
Introduction
GMAT divisibility questions test whether you can recognise factors, multiples and remainder patterns without relying on long division. These skills help you simplify large numbers, test prime factors and eliminate unsuitable answer choices in Quantitative Reasoning.
The current GMAT Quantitative Reasoning section contains 21 questions in 45 minutes and does not provide a calculator. In this blog, we explain the most useful GMAT divisibility rules, composite-number shortcuts, common mistakes and practice methods.
What Is GMAT Divisibility and Why Is It Tested?
A number is divisible by another integer when the division leaves a remainder of zero. For example, 42 is divisible by 7 because 42 ÷ 7 = 6 with no remainder.
GMAT divisibility is part of the broader number-properties topic. The official GMAT Quant skill classification includes factors, multiples, divisibility, prime numbers, greatest common factors and least common multiples.
These concepts may appear in questions involving several closely related number properties.
- Factors and multiples
- Prime and composite numbers
- Remainders
- Prime factorisation
- Powers and consecutive integers
- Algebraic expressions containing integers
You can review the official topic classification on the GMAT Quantitative Skill Groups page.
Which GMAT Divisibility Rules Should You Memorise?
Memorise the divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10, 11 and 12. The rule for 7 is also useful, although direct division or prime factorisation can sometimes be faster.
The following table brings together the most important GMAT divisibility rules and examples.
| Divisor | Divisibility Rule | Example |
|---|---|---|
| 2 | The last digit is 0, 2, 4, 6 or 8. | 746 is divisible by 2. |
| 3 | The sum of the digits is divisible by 3. | 714: 7 + 1 + 4 = 12. |
| 4 | The number formed by the last two digits is divisible by 4. | 1,236: 36 is divisible by 4. |
| 5 | The final digit is 0 or 5. | 2,315 is divisible by 5. |
| 6 | The number is divisible by both 2 and 3. | 534 is even and its digits total 12. |
| 7 | Double the final digit and subtract it from the remaining number. | 231: 23 − 2 = 21. |
| 8 | The number formed by the last three digits is divisible by 8. | 5,624: 624 ÷ 8 = 78. |
| 9 | The sum of the digits is divisible by 9. | 7,353: 7 + 3 + 5 + 3 = 18. |
| 10 | The final digit is 0. | 4,320 is divisible by 10. |
| 11 | The difference between the sums of alternating digits is 0 or a multiple of 11. | 2,915: (2 + 1) − (9 + 5) = −11. |
| 12 | The number is divisible by both 3 and 4. | 1,164 has a digit sum of 12 and 64 is divisible by 4. |
Divisibility by 2, 5 and 10
Check only the final digit. These are the fastest GMAT divisibility rules because no addition or long division is required.
Apply the following final-digit tests.
- An even final digit means the number is divisible by 2.
- A final digit of 0 or 5 means the number is divisible by 5.
- A final digit of 0 means the number is divisible by 10.
For example, 8,670 is divisible by 2, 5 and 10. However, 8,675 is divisible by 5 but not by 2 or 10.
Divisibility by 3 and 9
Add the digits and test the resulting sum. A number is divisible by 3 when its digit sum is divisible by 3. It is divisible by 9 when the digit sum is divisible by 9.
Consider the number 43,758.
- Digit sum: 4 + 3 + 7 + 5 + 8 = 27
- 27 is divisible by both 3 and 9
- Therefore, 43,758 is divisible by both 3 and 9
Every number divisible by 9 is also divisible by 3. However, a number divisible by 3 is not necessarily divisible by 9.
Divisibility by 4 and 8
For 4, examine the last two digits; for 8, examine the last three digits. The earlier digits do not affect these divisibility tests.
For example, 27,416 is divisible by 4 because 16 is divisible by 4. It is also divisible by 8 because 416 ÷ 8 = 52.
Divisibility by 7
Double the final digit and subtract it from the remaining digits. If the result is divisible by 7, the original number is also divisible by 7.
To test whether 511 is divisible by 7, follow these steps.
- Double the final digit: 1 × 2 = 2.
- Subtract it from 51: 51 − 2 = 49.
- 49 is divisible by 7.
- Therefore, 511 is divisible by 7.
For a small number, direct division may be faster. Use this shortcut when the original number is large enough to make division inconvenient.
Divisibility by 11
Find the difference between the sums of alternating digits. The number is divisible by 11 when that difference is zero or a multiple of 11.
For 2,915, apply the alternating-digit rule.
- First alternating sum: 2 + 1 = 3
- Second alternating sum: 9 + 5 = 14
- Difference: 3 − 14 = −11
- Therefore, 2,915 is divisible by 11
How Do Composite Divisibility Rules Work?
Break a composite divisor into suitable factors and test each required factor. A composite number has more than two positive factors.
The following combinations are useful in GMAT divisibility questions.
| Composite Divisor | Required Tests | Example |
|---|---|---|
| 6 | Divisible by 2 and 3 | 342 passes both tests. |
| 12 | Divisible by 3 and 4 | 468 passes both tests. |
| 15 | Divisible by 3 and 5 | 735 passes both tests. |
| 18 | Divisible by 2 and 9 | 1,458 passes both tests. |
| 24 | Divisible by 3 and 8 | 1,224 passes both tests. |
Testing divisibility by 3 and 6 is not sufficient for divisibility by 18 because these factors overlap. Use 2 and 9 because their least common multiple is 18.
How Do You Use Divisibility for Factors and Prime Numbers?
Use divisibility tests to identify small prime factors before performing full prime factorisation. If a number is divisible by a prime number, that prime is one of its factors.
Prime Factorisation
Prime factorisation expresses an integer as a product of prime numbers. This method is useful for questions involving factors, multiples, perfect squares, greatest common factors and least common multiples.
Consider 1,260:
1,260 = 2 × 630 = 2² × 315 = 2² × 3² × 5 × 7
The prime factorisation of 1,260 is therefore 2² × 3² × 5 × 7.
Prime Number Testing
Test only prime divisors up to the square root of the number. To determine whether 83 is prime, note that √83 is slightly greater than 9. You only need to test 2, 3, 5 and 7.
The following checks confirm whether 83 has a smaller prime factor.
- 83 is not even, so it is not divisible by 2.
- 8 + 3 = 11, so it is not divisible by 3.
- It does not end in 0 or 5.
- It is not divisible by 7.
Therefore, 83 is prime.
How Are GMAT Divisibility and Remainders Connected?
Divisibility means that the remainder is zero. If an integer does not divide evenly, the remainder shows the amount left after division.
For example:
1,234 = 11 × 112 + 2
Therefore, 1,234 leaves a remainder of 2 when divided by 11.
Digit Rules for Remainders
The digit-sum method can help find remainders involving 3 or 9. A number and its digit sum leave the same remainder when divided by 3 or 9.
For 4,357, apply the digit-sum method.
- Digit sum: 4 + 3 + 5 + 7 = 19
- 19 leaves remainder 1 when divided by 3
- Therefore, 4,357 also leaves remainder 1 when divided by 3
How Can You Solve GMAT Divisibility Questions Faster?
Identify the required divisor, factor it and apply the shortest suitable test. Avoid multiplying or dividing large numbers when a simple divisibility shortcut can answer the question.
Use the following process when solving GMAT divisibility questions.
- Read the condition: Determine whether the question asks about a factor, multiple, prime number or remainder.
- Factor the divisor: Rewrite a composite divisor using suitable factors.
- Apply the shortest test: Check the final digits before performing longer calculations.
- Use answer choices: Test the options when algebraic solving would take longer.
- Confirm every condition: Passing one test does not guarantee divisibility by a composite number.
Which GMAT Divisibility Mistakes Should You Avoid?
The most common mistake is applying only part of a composite-number rule. A number divisible by 3 is not automatically divisible by 6, 12 or 18.
Watch for the following errors during preparation and on test day.
- Testing only divisibility by 3 when the divisor is 6
- Checking the final two digits instead of three for divisibility by 8
- Assuming every odd number is prime
- Forgetting that 1 is neither prime nor composite
- Treating 0 as a valid divisor
- Confusing “a factor of” with “a multiple of”
- Ignoring negative differences in the divisibility test for 11
- Applying a memorised shortcut without checking whether it fits the divisor
How Do You Practise GMAT Divisibility Questions?
Practise in three stages: direct rule checks, mixed applications and timed problem solving. Learn each rule first and then use it in questions involving factors, primes and remainders.
Practice Question 1
Which of the following numbers is divisible by 12?
- 534
- 624
- 738
- 842
- 954
Answer: B. The digit sum of 624 is 12, so the number is divisible by 3. Its last two digits, 24, are divisible by 4. Therefore, 624 is divisible by 12.
Practice Question 2
What is the smallest digit that can replace x if 54x6 must be divisible by 9?
Answer: 3. The known digits total 5 + 4 + 6 = 15. The next multiple of 9 is 18, so x must equal 3.
Practice Question 3
If n is divisible by both 8 and 9, which of the following must divide n?
- 17
- 36
- 54
- 72
- 81
Answer: D. Since 8 and 9 are coprime, their least common multiple is 72. Therefore, n must be divisible by 72.
Practice Question 4
What remainder does 7,436 leave when divided by 9?
Answer: 2. The digit sum is 7 + 4 + 3 + 6 = 20, and 20 leaves remainder 2 when divided by 9.
Practice Question 5
Is 2,618 divisible by 7?
Answer: Yes. Double the final digit and subtract it from the remaining number: 261 − 16 = 245. Since 245 is divisible by 7, 2,618 is also divisible by 7.
Which Official Resources Should You Use for GMAT Practice?
Start with official GMAC questions after learning the divisibility rules. Official questions provide the closest representation of the reasoning, wording and difficulty used on the current GMAT.
The GMAT Official Starter Kit and Practice Exams 1 and 2 provide official practice material. GMAC’s official exam structure confirms that Quantitative Reasoning contains 21 questions in 45 minutes.
Use official questions to practise divisibility within broader number-property problems rather than expecting every question to ask for a direct divisibility check.
How Should Indian Applicants Prepare GMAT Divisibility?
Indian applicants should practise GMAT divisibility without a calculator and focus on application rather than memorisation alone. School-level familiarity with these rules can help, but GMAT questions may combine divisibility with factors, algebra, consecutive integers and remainders.
Maintain an error log that records the missed rule, the incorrect assumption and the faster solution method. Once direct questions become comfortable, move to mixed official Quant sets instead of continuing only with isolated calculations.
Related Blogs
- Properties of Integers for GMAT
- GMAT Integer Questions
- GMAT Quantitative Reasoning
- GMAT Arithmetic Tricks
Conclusion
GMAT divisibility becomes easier when you understand why each rule works and apply the shortest suitable test. Learn the core rules, practise composite divisors and connect divisibility with factors, primes and remainders before moving to timed mixed-question sets.
