GMAT® Divisibility Rules: A Complete Guide

Divisibility rules are old material, and the classics hold up: even numbers divide by 2, anything ending in 0 or 5 divides by 5, and the digit sum handles 3. You've been dividing since elementary school, so this can feel like a topic you finished years ago.

But the GMAT® rarely asks a bare question like "is 100 divisible by 4?" It hides divisibility inside questions about consecutive integers, lowest common multiples, and Data Sufficiency statements, and the packaging is where the difficulty lives. So the skill is bigger than a memorized list: which rules deserve a spot in memory, why the best ones work, and when to ignore the rules entirely and divide.

What divisibility means

A number is divisible by another when the division comes out clean: divide them and the result is an integer, with a remainder of zero.

$103 \div 10 = 10.3$

$100 \div 10 = 10$

So 100 is divisible by 10 and 103 is not. The exam phrases that same fact in several costumes, though. n is divisible by 5, n is a multiple of 5, and 5 is a factor of n all say the same thing, and a question can use any of them without slowing down to translate. Part of the skill is catching that a question about factors is really asking a division question.

Divisibility also sits at a crossroads. Primes, factors, multiples, and remainders all route through it, which is part of why the topic tends to appear inside questions that look like they're about something else. Our number properties guide covers that whole network. This guide sticks to the rules themselves: which ones to memorize, why the good ones work, and where long division fits.

The rules worth memorizing

Eight rules handle most of the divisibility the exam asks about, and they organize into families by how you check them:

Two of these families carry most of the divisibility questions we see, so they deserve a closer look.

The digit-sum rules: 3 and 9

If the digits of a number sum to a multiple of 3, the number is divisible by 3. If they don't, it isn't. The same test works one level up for 9: a digit sum that's a multiple of 9 means the number itself is a multiple of 9.

Is 1,032 divisible by 3? Add the digits: $1 + 0 + 3 + 2 = 6$, and 6 is a multiple of 3, so yes. Is 103? $1 + 0 + 3 = 4$, which isn't, so 103 leaves a remainder when you divide by 3.

The trick works because every power of 10 is exactly 1 more than a multiple of 9: ten is $9 + 1$, a hundred is $99 + 1$, a thousand is $999 + 1$. When you break a number into its place values, the multiples of 9 collect on one side and the digits collect on the other. Take 234:

$234 = (2 \times 99 + 3 \times 9) + (2 + 3 + 4)$

The first chunk is built from multiples of 9, so it divides by 9 and by 3. Everything rides on what's left, which is the digit sum $2 + 3 + 4 = 9$. Nine is a multiple of 3 and of 9, so 234 is divisible by both: $234 \div 3 = 78$ and $234 \div 9 = 26$. Once you've seen that, the two digit-sum rules tend to stay put.

The flip side is half the value. When the digit sum misses, you know the number isn't divisible, with no long division required. On a multiple-choice question, that means an answer choice can be eliminated in the time it takes to add three digits.

The last-digits rules: 4 and 8

A number is divisible by 4 when its last two digits form a multiple of 4, and by 8 when its last three digits form a multiple of 8. The number 2,316 is divisible by 4 because 16 is, and 2,520 is divisible by 8 because 520 is ($520 \div 8 = 65$).

These work like the digit-sum rules, just with bigger bricks. Since 100 is a multiple of 4, every full hundred in the number divides by 4, and the last two digits carry all the doubt. The same logic moves the decision to the last three digits for 8, because 1,000 is a multiple of 8. You're checking the smallest possible piece of the number instead of the whole thing.

The one that isn't worth it

Seven is the famous exception. Tricks for divisibility by 7 exist, and some of them are impressive in a listicle, but under time pressure a half-remembered trick can confuse a problem that plain division would solve. Our take, which we walk through in Episode 37 of our Real GMAT® Problems series ("Divisibility Shortcuts"), is to skip the tricks and divide by 7. Long division by a one-digit number is usually a few seconds of work when your mechanics are fresh.

Long division stays in the toolkit

There's a lot of advice in forums and prep courses about avoiding long division, as if it were a beginner's crutch to be outgrown. We come down on the other side: be good at long division. The rules and the mechanics aren't rivals. The rules can eliminate answer choices with no computation at all, and long division settles whatever survives.

The practical version: make sure your division mechanics are fresh enough to deploy under time pressure. That might take a few focused sessions if you haven't divided by hand in a while, and it's worth keeping a computation-heavy problem in your regular rotation so the skill stays warm. Every step added to a problem is an opportunity to make a mistake, and rusty arithmetic adds steps. The payoff shows up on questions like the one below, where the rules cut the field before any division starts and the division only has to finish the job.

Try this one

Try this one before reading on.

The question asks for a number that passes eight divisibility checks at once, which sounds like a lot of long division. The rules cut it down fast.

The 5 check is the cheapest, so start there: a number divisible by 5 ends in 0 or 5, and 3,024 ends in 4, so choice (B) is out. The 4 check works on the last two digits: 1,890 ends in 90, and 90 isn't a multiple of 4, so (D) is out. The 9 check uses the digit sum: $1 + 6 + 8 + 0 = 15$, which isn't a multiple of 9, so (E) is out.

That leaves (A) 15,120 and (C) 2,520, and both have cleared the rules for 2, 3, 4, 5, 6, and 9.

The table handles 8: (C)'s last three digits are 520, and $520 \div 8 = 65$. That leaves 7, which has no rule, so long division finishes it: $2{,}520 \div 7 = 360$, no remainder.

Now (C) has cleared every check, and (A), the only other survivor, is larger while passing the same checks. A larger number can't be the lowest, so the answer is (C).

This problem is retired from the 11th edition of the Official Guide. When we featured it on the podcast, 26 percent of listeners who tested themselves missed it, and 11 percent picked (A), a number divisible by everything in the list. That miss isn't a computation problem; it's a reading problem, where the word lowest gets lost somewhere between the question and the arithmetic. Writing down what's given and what's asked before any math is the habit that holds onto that word.

Where the test adds difficulty

Data Sufficiency, which lives in the Data Insights section, is divisibility's favorite wrapper. A statement like "n is divisible by 6" doesn't give you one number; it gives you a set of them: 6, 12, 18, 24, and so on. Sufficiency questions ask whether that set settles the matter, and often it doesn't. If the question asks whether n is divisible by 12, a statement that n is divisible by 6 leaves both doors open, since 6 itself is divisible by 6 but not by 12, while 12 is divisible by both. A statement that n is divisible by 24 would settle it, because every multiple of 24 is a multiple of 12. In Data Sufficiency, that's the whole game: divisibility statements hand you ranges of candidates, and you're scoring whether they pin anything down.

Remainders are the other frequent partner. Divisible means remainder zero, so every remainder question is a divisibility question with the leftover showing. The ones digit of a number is the remainder you get dividing by 10, and the last two digits hold the remainder when you divide by 100.

When two divisibility conditions stack, prime factors do the work. Divisible by 5 and by 7 adds up to divisible by 35, because the two primes share nothing. Our worked solution on a "divisible by both 5 and 7" question shows the method, and our rates and divisibility post covers the cancellation system that scales to bigger numbers.

Edge cases the exam likes

Zero is divisible by every nonzero integer, because $0 \div 5 = 0$ and 0 is an integer. Questions lean on this by offering 0 as a candidate that's easy to rule out on instinct, since "can you divide zero" sounds different from "does the division produce an integer." It does.

Negative numbers divide fine too. $-24$ is divisible by 4 because the result, $-6$, is an integer. The definition asks for an integer result, not a positive one. And 1 divides everything, which makes "n is divisible by 1" the least informative statement a Data Sufficiency question can offer.

FAQ

What are the divisibility rules for the GMAT®?

The core set: divisible by 2 if the last digit is even, by 3 if the digit sum is a multiple of 3, by 4 if the last two digits form a multiple of 4, by 5 if the number ends in 0 or 5, by 6 if it passes the 2 and 3 checks, by 8 if the last three digits form a multiple of 8, by 9 if the digit sum is a multiple of 9, and by 10 if it ends in 0.

How do you check if a number is divisible by 3?

Add the digits. If the sum is a multiple of 3, the number is divisible by 3, and if not, it isn't. For 1,032, the digit sum is $1 + 0 + 3 + 2 = 6$, so 1,032 is divisible by 3.

Is there a divisibility rule for 7?

There isn't one we'd recommend relying on. The tricks that circulate tend to cost as much time as they save under test pressure, so long division is the safer habit. By 7, dividing takes a few seconds when your mechanics are fresh.

How do divisibility rules show up in Data Sufficiency?

A statement like "n is divisible by 6" describes a set of possible values (6, 12, 18, and so on) rather than one value. The question is whether the statements narrow that set enough to settle the question asked, and a divisibility statement alone often doesn't.

Is 0 divisible by other numbers?

Yes. Zero divided by any nonzero integer gives 0, which is an integer, so 0 is divisible by 2, by 5, by 9, etc.

Do you need divisibility rules on the GMAT® Focus Edition?

They're worth having. The quant section is calculator-free, with 21 Problem Solving questions in 45 minutes, and Data Insights adds Data Sufficiency on top. Divisibility checks convert slow divisions into fast ones, and fast ones help protect the clock.

Want to learn even more?

Related reading:

• GMAT® Number Properties: A Complete Guide
• GMAT® Data Sufficiency: How to Approach DS Questions
• GMAT® Rates and Divisibility: Two Systems That Scale
• GMAT® Permutations and Combinations: A Complete Guide
• "If a Positive Integer n Is Divisible by Both 5 and 7..." — GMAT® Worked Solution

The Math Basics series includes a full podcast lesson on divisibility, "GMAT® Focus Edition Math Basics: Divisibility" (Lesson 4 in the series), and Episode 37 of our Real GMAT® Problems series, "Divisibility Shortcuts," works through three Official Guide problems using these rules. You can hear both on Spotify, Apple Podcasts, or YouTube.