Number System is usually the first topic CAT aspirants study, and there’s a good reason for it—it’s built on rules and not judgment calls. Divisibility, remainders, factors, and unit digits all follow fixed logic, so once you’ve internalized the patterns, the marks here are some of the most consistent in the whole Quant section. This CAT 2026 Number System Practice guide has the most important number system questions to practice, weightage trends, a quick formula cheat sheet, and a practice strategy you can start using right now
We’ve pointed this out clearly where appropriate. Build Number System from scratch or sharpen up before your next mock; treat this as a working reference rather than another static formula list.
CAT does not publish an official syllabus, so everything about weightage here is based on analyzing recent CAT papers rather than a confirmed exam blueprint—we’ve flagged this clearly wherever it applies.
Table of Contents
- Why Number System Is Important for CAT 2026
- Important Number System Topics
- Top Number System Questions with Solutions
- Common Mistakes to Avoid
- How to Prepare Number System for CAT 2026
- Practice 600+ Number System Questions with CatMock Bhandara
- FAQs
Why Number System Is Important for CAT 2026
Number System covers Divisibility Rules, Factors & Multiples, HCF & LCM, Remainders & Cyclicity, Base Systems, and Factorials. Estimates on exact weightage vary by source, but most place it around 3 to 5 questions out of the 22 in CAT Quant—a smaller slice than Arithmetic or Algebra, but a genuinely high-value one.
Here’s why: Number System questions rarely require multi-step reasoning once you know the underlying property. A divisibility question is either a quick rule-check or it isn’t. A remainder question almost always reduces to spotting a cycle. That makes this topic one of the best places in the entire QA section to bank fast, confident marks—freeing up time for genuinely harder Algebra or Geometry problems later.
It also quietly supports other topics. HCF/LCM logic resurfaces in Time & Work and Time-Speed-Distance problems, and prime factorization skills make Algebra’s polynomial questions faster to crack. Strengthening Number System isn’t just about this topic’s own weightage—it sharpens your overall numerical instincts.
Important Number System Topics
Here’s how Number System typically breaks down in a CAT paper, based on trends from recent years:
Table 1: Number System Topic-Wise Weightage for CAT 2026
| Number System Topic | Avg. Questions in CAT | Difficulty Level | Prep Priority |
|---|---|---|---|
| Divisibility Rules & Factors | 1 | Low | High |
| HCF & LCM | 1 | Low–Moderate | High |
| Remainders & Cyclicity | 1–2 | Moderate | Highest |
| Base Systems | 0–1 | Moderate | Medium |
| Factorials (Trailing Zeros) | 0–1 | Low–Moderate | Medium |
| Prime Numbers & Number Properties | 1 | Low–Moderate | Medium |
Remainders and cyclicity consistently carry the most weight and the most difficulty within this topic—CAT loves dressing up a simple remainder question with a large exponent or an unusual base, so this is the sub-topic worth the deepest practice.
Essential Number System Shortcuts Worth Memorizing
A handful of shortcuts do most of the heavy lifting in this topic. Know these cold, and a large share of Number System questions turn into 30-second solves instead of 3-minute ones.
Table 2: Must-Know Number System Shortcuts for CAT 2026
| Shortcut | Rule | Where It Shows Up |
|---|---|---|
| Number of factors | For N = a^p × b^q × c^r, factors = (p+1)(q+1)(r+1) | Factor-count questions (like Q2) |
| HCF × LCM rule | For exactly two numbers, HCF × LCM = product of the numbers | HCF/LCM problems (like Q3) |
| Cyclicity of unit digits | Digits 2, 3, 7, 8 repeat every 4 powers; 4, 9 repeat every 2; 0, 1, 5, 6 never change | Remainder and unit-digit problems (like Q4) |
| Trailing zeros in n! | Sum of ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + … | Factorial questions (like Q6) |
| Base conversion | Divide repeatedly by the target base; read remainders bottom-up | Base system problems (like Q5) |
| Divisibility by 9 / 3 | A number is divisible by 9 (or 3) if its digit sum is divisible by 9 (or 3) | Quick divisibility checks under time pressure |
Notice how directly these map to the worked questions above—most Number System questions are really just “which shortcut applies here” once you strip away the word-problem framing.
Top Number System Questions with Solutions
These questions aren’t reproduced from any specific CAT paper — they’re original problems built to mirror the exact patterns CAT keeps testing year after year. Solve each one before checking the solution.
1. Divisibility
Q1. Find the smallest number that must be added to 1,000 to make it exactly divisible by 27.
Divide 1,000 by 27: 27 × 37 = 999, leaving a remainder of 1. The smallest number to add = 27 − 1 = 26
Answer: 26
2. Factors & Multiples
Q2. Find the number of factors of 720.
Prime factorize: 720 = 2⁴ × 3² × 5¹ Number of factors = (4+1)(2+1)(1+1) = 5 × 3 × 2 = 30
Answer: 30 factors
3. HCF & LCM
Q3. The HCF and LCM of two numbers are 12 and 504 respectively. If one of the numbers is 72, find the other number.
Product of two numbers = HCF × LCM = 12 × 504 = 6,048 Other number = 6,048 ÷ 72 = 84
Answer: 84
4. Remainders & Cyclicity
Q4. Find the remainder when 7⁴⁵ is divided by 5.
7 mod 5 = 2, so we need the cycle of 2ⁿ mod 5: 2, 4, 3, 1 (repeats every 4 powers). 45 mod 4 = 1, so 2⁴⁵ mod 5 behaves like 2¹ mod 5.
Answer: 2
5. Base Systems
Q5. Convert the decimal number 156 into base 6.
156 ÷ 6 = 26, remainder 0 26 ÷ 6 = 4, remainder 2 4 ÷ 6 = 0, remainder 4. Reading remainders bottom-up: 156 in base 6 = 420
Answer: 420 (base 6)
6. Factorials
Q6. Find the number of trailing zeros in 125!.
Trailing zeros come from factors of 5 (since factors of 2 are always in excess): ⌊125/5⌋ + ⌊125/25⌋ + ⌊125/125⌋ = 25 + 5 + 1 = 31
Answer: 31 trailing zeros
7. Prime Numbers
Q7. How many prime numbers are there between 50 and 100?
Listing primes in this range: 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Answer: 10 prime numbers
8. LCM Word Problem
Q8. Three bells ring at intervals of 12, 18, and 24 minutes respectively. If they all ring together at 8:00 AM, at what time will they next ring together?
Find the LCM of 12, 18, and 24: 12 = 2² × 3, 18 = 2 × 3², 24 = 2³ × 3 LCM = 2³ × 3² = 72 The bells next ring together after 72 minutes, i.e., at 9:12 AM
Answer: 9:12 AM
Table 3: Quick Answer Key
| Q. No. | Topic | Final Answer |
|---|---|---|
| Q1 | Divisibility | 26 |
| Q2 | Factors & Multiples | 30 factors |
| Q3 | HCF & LCM | 84 |
| Q4 | Remainders & Cyclicity | 2 |
| Q5 | Base Systems | 420 (base 6) |
| Q6 | Factorials | 31 trailing zeros |
| Q7 | Prime Numbers | 10 primes |
| Q8 | LCM Word Problem | 9:12 AM |
Common Mistakes to Avoid
- Forgetting that “smallest number to add” and “smallest number to subtract” for divisibility use different arithmetic—mixing these up flips your answer.
- Miscounting factors by forgetting to add 1 to each exponent in the prime factorization before multiplying.
- Assuming HCF × LCM = product of numbers works for more than two numbers — this identity only holds for exactly two numbers.
- Losing track of the cycle length in remainder problems, especially when the exponent is large—always find the cycle first, then reduce the exponent using the modulus of the cycle length.
- Rushing base-conversion problems without double-checking the final digit order—remainders come out least-significant-digit first, so they must be reversed.
How to Prepare Number System for CAT 2026
Number System is one of the fastest topics to get genuinely good at—a focused 3-week block, run alongside your Arithmetic and Algebra prep, is usually enough to cover every major sub-topic with real confidence.
Table 4: 3-Week Number System Prep Plan
| Week | Focus Area | Daily Target |
|---|---|---|
| Week 1 | Divisibility Rules, Factors & Multiples, HCF & LCM | 12 questions/day + rule revision |
| Week 2 | Remainders & Cyclicity — the highest-difficulty sub-topic | 10 questions/day, mixed difficulty |
| Week 3 | Base Systems, Factorials, Prime Numbers + full mixed-topic mock sets | 1 sectional mock every 2 days |
Practice 600+ Number System Questions with CatMock Bhandara
Bhandara by CatMock is a structured, topic-wise question bank built specifically for CAT aspirants — so you always know exactly what to solve next, instead of hunting across ten different sites.
Inside Bhandara, you’ll get:
- 600+ Number System Questions
- 700+ Arithmetic Questions
- 700+ Algebra Questions
- 600+ Modern Mathematics Questions
- 600+ Mensuration Questions
- 500+ Geometry Questions
Bhandara is your complete CAT preparation treasure
Everything you need, all in one place.
Stop Searching for Number System Questions. Start Solving the Right Ones.
Number System is one of the quickest wins available in CAT Quant—but only if you actually put in the reps instead of skimming concept videos and assuming it’ll click on exam day. Divisibility, HCF & LCM, and remainders show up every single year, and the aspirants who drill these patterns consistently are the ones finishing this section with time to spare for harder topics.
Stop bouncing between scattered PDFs and half-finished question sets. Practice from one structured collection of 600+ CAT-level Number System questions, organized so you can build fundamentals, spot weak areas fast, and move confidently into exam-difficulty problems.
Whether you’re learning divisibility rules for the first time or sharpening remainder shortcuts before mocks, a focused question bank is what turns “I get the concept” into “I solved that in 40 seconds.” That gap is exactly what separates an average QA score from a strong one.
Explore Number System Bhandara and master every important topic with 600+ carefully curated CAT-level questions.
FAQs
What is the weightage of Number System in CAT 2026?
Number System typically contributes 3 to 5 questions out of the 22 questions in CAT’s Quant section, spread across Divisibility, Factors & Multiples, HCF & LCM, Remainders & Cyclicity, Base Systems, and Factorials.
Which topics are covered under Number System for CAT 2026?
A number system includes Divisibility Rules, Factors & Multiples, HCF & LCM, Remainders & Cyclicity, Base Systems, Factorials (Trailing Zeros), and Prime Numbers & Number Properties.
Are CAT Number System questions repeated from previous years?
The exact questions are not repeated, but the underlying patterns—large-exponent remainder problems, factor-count questions, base conversions, LCM-based word problems—show up year after year, which is why practising these patterns pays off.
How many Number System questions should I attempt in CAT?
Attempting 3 to 4 well-chosen Number System questions with high accuracy is a reasonable target for most aspirants, since these questions tend to be faster to solve than Algebra or Geometry once the fundamentals are strong.
Where can I find enough practice questions for Number System?
CatMock’s QA Bhandara has 600+ dedicated Number System questions, along with thousands more across every other Quant topic, for structured, topic-wise practice.
Is Number System difficult for CAT?
Not usually. Most Number System questions rely on a small set of properties and rules rather than heavy calculation. With consistent practice, this topic often becomes one of the fastest, most reliable scoring areas in CAT Quant.
Conclusion
Number System is, quietly, one of the best-value topics in the entire CAT Quant syllabus. The concepts are finite, the tricks are learnable in weeks rather than months, and the questions that do appear are consistently some of the fastest to solve in the whole section. Work through the questions above, follow the 3-week plan, and drill remainders and cyclicity until spotting the pattern becomes automatic—well before CAT 2026 arrives on 29 November. A sharp Number System base is an easy, reliable way to bank marks before you even reach the harder parts of Quant.
