If you're studying for the GMAT® and you keep missing questions about odds, evens, primes, and divisibility, that makes sense.
Number properties questions can feel like a different language. There's no advanced algebra or calculus. But the questions ask you to reason about how numbers behave — and that's a skill a lot of us haven't used in years.
The good news is that number properties questions follow patterns. Once you learn the core rules and build a system for testing them, most of these questions become manageable.
What follows are the key concepts, the rules worth memorizing, and a testing-numbers method that handles the majority of number properties questions on the GMAT® Focus Edition.
What Are Number Properties on the GMAT®
Number properties questions test your understanding of how numbers behave. Instead of asking you to solve an equation, they ask you to determine whether a statement must be true, could be true, or cannot be true based on given constraints.
On the GMAT® Focus Edition, number properties appear in the Quantitative section (Problem Solving and Data Sufficiency) and sometimes in Data Insights. The core topics are:
- Primes
- Odds and evens
- Divisibility
- Factors and multiples
- Remainders
You won't see a question that says "define a prime number." Instead, you'll see a problem that requires you to use prime concepts to reach a conclusion. The test is about applying these ideas, not reciting them.
If you want a full breakdown of what's on each section, our complete GMAT® topic list covers every topic you need to know.
Primes
A prime number has exactly two distinct factors: 1 and itself. That's the definition the GMAT® uses, and it comes with a few implications worth noting.
One isn't prime. It has only one factor. Two is the smallest prime, and it's the only even prime. Every other even number has at least three factors (1, 2, and itself), so no even number greater than 2 is prime.
The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
If you're aiming for a top score — a 655 or higher on the Focus Edition — we suggest memorizing all primes up to 100. It takes a little time, but it pays off. You'll recognize primes faster, work with more confidence under pressure, and avoid spending precious seconds deriving whether 51 is prime (it's not — it's 3 times 17).
If you're aiming for a lower target score, you can figure out primes one at a time as needed. But for top scorers, memorization up to 100 is worth the investment.
How to Test Whether a Number Is Prime
To check if a number is prime, try dividing it by primes up to its square root. If none divide evenly, the number is prime.
For example, is 53 prime?
The square root of 53 is between 7 and 8. So we only need to test primes up to 7: that's 2, 3, 5, and 7.
53 isn't even, so 2 doesn't work. The sum of the digits (5 plus 3) is 8, which isn't a multiple of 3, so 3 doesn't work. 53 doesn't end in 0 or 5, so 5 doesn't work. And 53 divided by 7 gives 7 with a remainder of 4, so 7 doesn't work.
None of them divide evenly. 53 is prime.
This process gets faster with practice. After a few rounds, you'll start recognizing primes on sight.
Odds and Evens
Odd and even rules are straightforward once you've seen them. The challenge isn't learning the rules — it's applying them under pressure without making a mistake.
Here are the core rules:
Odd plus odd is even. Even plus even is even. Odd plus even is odd.
Odd times odd is odd. Even times anything is even.
That last one is worth pausing on. Even times anything is even. If one factor in a product is even, the entire product is even. This comes up on the GMAT® more than almost any other number properties rule.
Consecutive Integers
The product of two consecutive integers is always even. That's because one of them must be even.
The product of three consecutive integers is always divisible by 6. That's because among any three consecutive integers, at least one is even (so the product is divisible by 2) and at least one is a multiple of 3 (so the product is divisible by 3).
These patterns show up on the GMAT® in questions like: "If n is a positive integer, is n times (n plus 1) times (n plus 2) divisible by 4?" You could try to reason about this theoretically. But there's a more reliable approach, which we'll get to shortly.
Divisibility
Divisibility questions ask whether one number divides evenly into another. The GMAT® loves divisibility because it connects to primes, factors, multiples, and remainders all at once.
Here are the divisibility rules worth knowing:
Divisible by 2: the number is even. Divisible by 3: the sum of the digits is a multiple of 3. Divisible by 4: the last two digits form a number divisible by 4. Divisible by 5: the number ends in 0 or 5. Divisible by 6: the number is divisible by both 2 and 3. Divisible by 9: the sum of the digits is a multiple of 9. Divisible by 10: the number ends in 0.
The divisibility-by-3 rule is the one we use most often on the GMAT®. If the sum of the digits of a number equals a multiple of 3, the number is divisible by 3. And the flip side: if the sum of the digits isn't a multiple of 3, the number isn't divisible by 3.
For example, is 103 divisible by 3? Add the digits: 1 plus 0 plus 3 equals 4. Four isn't a multiple of 3, so 103 isn't divisible by 3.
This shortcut saves time on problems where you'd otherwise need long division. In Episode 37 of our podcast series, Real GMAT® Problems, we walk through several divisibility problems using this exact shortcut.
Factors and Multiples
A factor is a number that divides evenly into another number. A multiple is what you get when you multiply a number by an integer.
For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. The multiples of 12 are 12, 24, 36, 48, and so on.
Here's a mindset shift that can help on the GMAT®. Instead of thinking about multiples in terms of multiplication, think about them in terms of division. If you need to know whether 103 is a multiple of 10, ask yourself: does 103 divided by 10 give an integer? It doesn't, so 103 isn't a multiple of 10.
This approach is faster for most people than trying to list all the multiples of 10 and checking whether 103 appears. It's especially helpful when the number in question is large or the divisor is something like 19, where the multiples aren't obvious.
Factor Trees and Prime Factorization
Every integer greater than 1 can be written as a product of primes. This is called prime factorization, and it's one of the most useful tools on the GMAT®.
To find the prime factorization of a number, keep dividing by primes until you can't anymore. A factor tree helps you stay organized.
For example, the prime factorization of 36:
36 equals 4 times 9. 4 equals 2 times 2. 9 equals 3 times 3.
So 36 equals 2 times 2 times 3 times 3, or .
Prime factorization helps you answer questions about divisibility, greatest common factor, and least common multiple. If two numbers share the same prime factors, you can compare them quickly without doing long division.
Remainders
A remainder is what's left over when you divide one number by another and the result isn't a whole number.
For example, 17 divided by 5 is 3 with a remainder of 2. The quotient is 3, and 2 is what's left over.
On the GMAT®, remainder questions often show up in Data Sufficiency format. You might see something like: "When n is divided by 5, the remainder is r. What is r?"
The key insight is that a remainder is always less than the divisor. If you're dividing by 5, the remainder can only be 0, 1, 2, 3, or 4. It can never be 5 or higher.
Another useful pattern: if you add two numbers and then divide by k, the remainder equals the sum of the individual remainders (minus k if the sum is too large). This comes up on questions that ask about the remainder of a sum.
The Testing Numbers Method
Here's where everything comes together.
Most number properties questions on the GMAT® can be solved by testing numbers. Instead of trying to reason through the theory in your head, you pick small values that fit the constraints, plug them in, and see what happens.
This approach is more reliable than pure theory for most people. The reason is simple: when you reason in your head, you have to keep track of multiple constraints at once. One missed constraint means a wrong answer. When you test numbers on paper, the numbers do the tracking for you.
We cover this system in detail in Episode 38 of our podcast series, Real GMAT® Problems — The Power of Testing Numbers, and in our guide on testing numbers as a GMAT® strategy. Here's the shortened version.
Step 1: Write What's Given and What's Asked
Before you start testing anything, write down what the problem tells you and what it asks. This sounds obvious, but skipping it is one of the most common reasons people miss number properties questions. When you don't have a written system for capturing what the problem gives you, it's easy to drop a constraint without noticing.
Step 2: Pick Small, Simple Numbers
Start with the smallest numbers that fit the constraints. If the question involves odd and even, try 1 (odd) and 2 (even). If it involves primes, try 2, 3, and 5. If it involves divisibility by 3, try 3, 6, and 9.
Small numbers are faster to compute and less prone to arithmetic errors.
Step 3: Test One Number Against All Answer Choices
Before you pick your second number, run your first number against all five answer choices. This way, you eliminate as many options as possible with a single test.
For example, if a question asks about and you plug in :
Now check each answer choice against 6. If an answer says "even only when n is even," you can eliminate it — because n is 1 (odd) and the result is even.
Step 4: Pick a Second Number to Confirm
After eliminating what you can, pick a second number that's different enough from the first to test the remaining answer choices. If your first number was odd, try an even one. If your first was 1, try 2 or 3.
One number usually isn't enough. Two numbers almost always narrows it down to one answer.
Step 5: Organize Your Work Visually
Give each answer choice its own row or column on your scratch pad. Write the letter, plug in the number, and do the math in that row. Cross off eliminated answers with a clear X.
This organization matters more than most people think. On harder number properties questions, the constraints stack up. If your work is scattered, you lose track of what you've tested and what you haven't. If it's organized, you can review your steps quickly and catch mistakes.
If you want to see this system applied to real GMAT® problems, the testing numbers guide walks through three official problems step by step.
Common Number Properties Traps
Trap 1: Assuming What's True for One Case Is Always True
Just because a pattern holds for doesn't mean it holds for all values of n. This is why testing two numbers is important. The first number eliminates obviously wrong answers. The second number catches the ones that worked by coincidence.
Trap 2: Forgetting That 1 Is Not Prime
The GMAT® definition of prime is a number with exactly two distinct factors. One has only one factor, so it's not prime. This comes up in questions that ask about sums of primes or products of primes. If you include 1, you'll get the wrong answer.
Trap 3: Forgetting That 2 Is the Only Even Prime
Every even number greater than 2 has at least three factors (1, 2, and itself). So if a question says "p is a prime number greater than 2," you can assume p is odd. This inference shows up frequently.
Trap 4: Reasoning in Your Head
This is the most common trap of all. Number properties questions are designed to have multiple moving parts. The more constraints a problem has, the more likely you're going to drop one while reasoning mentally. Writing things down isn't slower — it's faster, because you avoid the need to retrace your steps when you lose track.
How to Practice Number Properties
Start with the official GMAT® guides. Official problems are the closest representation of what you'll see on test day, and the Official Guide has plenty of number properties questions across difficulty levels.
When you practice, use the testing numbers method on every number properties question — even the easy ones. The goal isn't just to get the right answer. It's to build the habit so deeply that it happens automatically on test day.
After each problem, review your work. Did you test the right numbers? Did you organize your scratch pad? Did you miss a constraint? This review process is where the improvement happens. Our guide on how to review GMAT® practice tests walks through a three-layer review system that works for individual problem sets too.
If number properties questions feel intimidating right now, that's normal. They're a new way of thinking about math for most people. Our guide on building GMAT® quant confidence covers how to get comfortable with quant topics that feel out of reach.
Frequently Asked Questions
What are number properties on the GMAT®?
Number properties questions test how well you understand how numbers behave. The core topics are primes, odds and evens, divisibility, factors and multiples, and remainders. You won't be asked to define these terms directly. Instead, you'll need to apply them to determine whether a statement must be true, could be true, or cannot be true.
Do you need to memorize prime numbers for the GMAT®?
For most score targets, you don't need to memorize primes. You can derive them as needed by testing divisibility. For students aiming for 655 or higher, memorizing all primes up to 100 can save time and reduce errors under pressure.
What's the fastest way to solve number properties questions on the GMAT®?
For most people, the testing numbers method is the fastest and most reliable approach. Pick small values that fit the constraints, plug them into each answer choice, and eliminate. Two well-chosen numbers usually narrow the answer to one option. This is more reliable than reasoning through number theory in your head, especially on harder questions with multiple constraints.
Is 1 a prime number?
No. By the GMAT® definition, a prime number has exactly two distinct factors. One has only one factor (itself), so it's not prime. Two is the smallest prime, and it's the only even prime.
How many number properties questions will I see on the GMAT®?
The exact number varies, but you can expect number properties concepts to appear in a meaningful portion of the Quantitative section. They may show up as Problem Solving questions, Data Sufficiency questions, or within Data Insights. Building a strong foundation in number properties can change how you approach the entire quant section — fewer dropped constraints, less wasted time on long division, and more confidence on questions that used to feel like a guessing game.
Should you use number theory or testing numbers on the GMAT®?
Both approaches can work. Testing numbers is more reliable for most people because it reduces the chance of dropping a constraint in your head. If you're someone who can reason through number theory with near-perfect accuracy, that approach can be faster. But that's rare. For the vast majority of test takers, testing numbers produces better results with fewer mistakes.
Want to learn even more?
Number properties are one piece of the GMAT® quant puzzle. If you're building your study plan, start with our guide on how to study for the GMAT® and our complete GMAT® topic list.
For more on the testing numbers method, listen to Episode 38 of our podcast series, Real GMAT® Problems — The Power of Testing Numbers on Spotify, Apple Podcasts, or YouTube.
If you're stuck on a specific quant topic and considering a tutor, our guide on how to build GMAT® quant confidence can help you decide whether you need one.