Rule of Divisibility Tests — Pick a Level and Start
Tap a level to see every test in it. Start at Level 1 the day you finish the rules, then move to Level 2 with the timer running to push accuracy under pressure.
Level 1 Basic Checking… View tests
Direct use of a single rule — is the number divisible by 4, 6, 8, 9 or 11, find the missing digit, and the smallest number to add or subtract. Attempt these without the clock while the rules are still fresh.
Level 2 Tier I Standard Checking… View tests
Real SSC CGL Tier I difficulty — rules for 7, 13, 17 and 19, composite divisors split into co-prime factors, two unknown digits at once, and the first algebraic divisibility questions. This is the score that tells you the chapter is exam-ready.
The rule of divisibility is the smallest chapter in the SSC CGL Quantitative Aptitude syllabus by direct weight and one of the most valuable by indirect weight. A shift may carry only one question that names divisibility outright — usually a missing digit or a smallest number to add — but the same rules are what let you cancel a fraction on sight, spot a factor without dividing, and shorten an LCM, remainder or simplification question that would otherwise eat a minute.
These practice tests put fifty divisibility questions in front of you in one sitting, which is what turns the rules from something you can recite into something you apply without thinking. Every question comes with a full solution and the shortcut, in English or Hindi.
How Many Divisibility Questions Are Asked in SSC CGL?
Divisibility rarely gets a question to itself. It sits underneath the whole arithmetic block, and that block together is worth four to six marks in a typical Tier I shift.
| Chapter | Tier I (out of 25) | Tier II Paper I (out of 30) |
|---|---|---|
| Rule of Divisibility | 0–1 | 0–1 |
| Number System | 2–3 | 3–4 |
| LCM & HCF | 1–2 | 1–2 |
| Remainder Theorem | 0–1 | 1 |
| Simplification | 1–2 | 2–3 |
Typical spread across recent SSC CGL shifts. SSC does not publish a chapter-wise breakup, so treat these as planning ranges. Tier I maths is always 25 questions in a locked 15-minute section.
What You Will Practice in the Rule of Divisibility Chapter
Core topics
- Divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10 and 11
- Rules for 7, 13, 17 and 19 by the multiply-and-adjust method
- Divisibility by 16, 25 and 125 from the last few digits
- Composite divisors such as 12, 15, 18, 24, 36, 45, 72 and 88, split into co-prime factors
- Missing digit questions — one unknown digit, and two unknown digits with two conditions
- The smallest number that must be added to or subtracted from a number to make it divisible
- Divisibility of an − bn and an + bn
- Divisibility of expressions and of products of consecutive integers
- The largest number that always divides a given expression
- Using divisibility to test whether a given option can be the answer
Divisibility rules you must know cold
| Divisor | Rule |
|---|---|
| 2 | Last digit is even |
| 3 | Sum of the digits is divisible by 3 |
| 4 | Last two digits form a number divisible by 4 |
| 5 | Last digit is 0 or 5 |
| 6 | Divisible by both 2 and 3 |
| 8 | Last three digits form a number divisible by 8 |
| 9 | Sum of the digits is divisible by 9 |
| 10 | Last digit is 0 |
| 11 | Difference between the sum of digits in odd and even places is 0 or a multiple of 11 |
| 16 | Last four digits form a number divisible by 16 |
| 25 | Last two digits are 00, 25, 50 or 75 |
| 125 | Last three digits form a number divisible by 125 |
The awkward ones — 7, 13, 17 and 19
Each of these has the same shape. Chop off the last digit, do one small operation with it, and repeat on the shorter number until you can judge it by sight.
| Divisor | What to do with the last digit | Example |
|---|---|---|
| 7 | Double it and subtract from the rest | 8232 → 823 − 4 = 819 → 81 − 18 = 63 ✔ |
| 13 | Multiply by 4 and add to the rest | 2197 → 219 + 28 = 247 → 24 + 28 = 52 ✔ |
| 17 | Multiply by 5 and subtract from the rest | 221 → 22 − 5 = 17 ✔ |
| 19 | Double it and add to the rest | 209 → 20 + 18 = 38 ✔ |
In the exam you will almost never need the rule for 7 more than twice on the same number. If it is still large after two rounds, the intended method was probably something else.
Composite divisors — split into co-prime factors
| Divisor | Test these two | Do not use |
|---|---|---|
| 12 | 3 and 4 | 2 and 6 |
| 15 | 3 and 5 | — |
| 18 | 2 and 9 | 3 and 6 |
| 24 | 3 and 8 | 4 and 6 |
| 36 | 4 and 9 | 6 and 6 |
| 45 | 5 and 9 | 3 and 15 |
| 88 | 8 and 11 | 4 and 22 |
The two factors must be co-prime, meaning their HCF is 1. This is the single most common trap in the chapter: 18 is divisible by 2 and by 6, yet it is not divisible by 12.
Algebraic divisibility — the four results
| Expression | Divisible by | When |
|---|---|---|
| an − bn | a − b | For every n |
| an − bn | a + b | Only when n is even |
| an + bn | a + b | Only when n is odd |
| an + bn | a − b | Never |
Also worth memorising
- The product of any
nconsecutive integers is divisible byn!— son(n+1)(n+2)is always divisible by 6 n³ − nis always divisible by 6, andn⁵ − nby 30- A number is divisible by 99 if the sum of its digits taken in pairs from the right is divisible by 99
- A number is divisible by 999 if the sum of its digits taken in threes from the right is divisible by 999
- Smallest number to add = divisor − remainder; smallest number to subtract = the remainder itself
Solved Examples — SSC CGL Rule of Divisibility
How the Divisibility Chapter Tests Work
- 50 questions per test, with a full question palette — answered, skipped, marked for review, not visited.
- Optional 30-minute timer — with the clock to build exam speed, without it while you are still learning the rules.
- Marking: +2 correct, −0.5 wrong, 0 unattempted — the same scheme as the real paper.
- Solutions, shortcut tricks and concept notes open after you submit, question by question.
- English and हिंदी, chosen at the start of every test.
- Free with a TrickySSC account — sign in once with Google or your mobile number, and every test is open to you.
How to Prepare the Rule of Divisibility for SSC CGL
- Learn the rules for 2 to 11 first and test them on phone numbers. They cost nothing to practise and they are the ones that appear inside other chapters.
- Treat 7, 13, 17 and 19 as one method, not four rules. All four chop the last digit and adjust; only the multiplier and the sign change. Learning them as a family takes a fraction of the time.
- Always split a composite divisor into co-prime factors. Most wrong answers in this chapter come from testing 12 as 2 and 6, or 24 as 4 and 6.
- Do Level 1 untimed, the same day you finish the rules. The aim is correct recall, not speed.
- Move to Level 2 with the 30-minute clock on. A divisibility question that takes more than thirty seconds means you are still dividing instead of testing.
- Study it as a block. Do number system, LCM and HCF and remainder theorem right after — they reuse these rules constantly.
- Verify against a real paper. Once Level 2 is consistent, attempt a previous year paper and then a full mock test under locked sectional timing.
SSC CGL विभाज्यता के नियम (Rule of Divisibility) चैप्टर टेस्ट — हिंदी में
विभाज्यता के नियम SSC CGL गणित का सबसे छोटा अध्याय है, लेकिन इसका उपयोग सबसे ज़्यादा होता है। सीधे तौर पर हर शिफ्ट में 0–1 प्रश्न आता है — जैसे लुप्त अंक ज्ञात करना या सबसे छोटी संख्या जोड़ना — पर यही नियम संख्या पद्धति, लघुत्तम-महत्तम, शेषफल और सरलीकरण के प्रश्नों में बार-बार काम आते हैं।
TrickySSC पर इस अध्याय के सभी टेस्ट हिंदी में उपलब्ध हैं — प्रश्न, विकल्प, विस्तृत हल और शॉर्टकट ट्रिक सब हिंदी में। दो स्तर हैं: लेवल 1 (आधारभूत) और लेवल 2 (टियर I स्तर)। प्रत्येक टेस्ट में 50 प्रश्न, वैकल्पिक 30 मिनट का टाइमर और +2 / −0.5 की वही मार्किंग जो असली परीक्षा में होती है।
ध्यान रखने योग्य बात: 12, 24, 36 जैसी भाज्य संख्याओं के लिए हमेशा सह-अभाज्य गुणनखंडों से जाँच करें — 12 के लिए 3 और 4, 24 के लिए 3 और 8। 12 को 2 और 6 से जाँचना ग़लत है, क्योंकि 18 दोनों से विभाजित होती है फिर भी 12 से नहीं।