Number System & Simplification: The Speed Chapter for RRB NTPC
Learn to sort numbers by type, apply divisibility shortcuts, crack LCM and HCF, and simplify with BODMAS — the fast, low-effort marks that lift your RRB NTPC maths score.
By the PadhoDost Team · 📖 7 min read · Updated 4 August 2026
Part of Railway Exams (RRB) prep🧠 Your kitchen dabba shelf
Think of numbers in maths like the dabbas in your kitchen. You keep dal in one, rice in another, masala in a third. Nothing is thrown together randomly. The Number System works exactly like this: every number has a shelf it belongs to (natural, whole, prime, even...), and once you know the shelves, you can grab the right one in seconds. In the RRB NTPC exam, that speed is everything. Padho, dost — let us organise the shelf together.
Part 1: Types of Numbers
Before you solve anything, you must recognise what kind of number you are looking at. Counting numbers (1, 2, 3...) are Natural numbers. Add zero and you get Whole numbers. Add the negatives too and you get Integers. A Prime number has exactly two factors (1 and itself), while a Composite number has more than two. This is basic, but examiners love to trap you on the edge cases, so read the table slowly.
| Type | Meaning | Examples |
|---|---|---|
| Natural (N) | Counting numbers, starting from 1 | 1, 2, 3, 4 ... |
| Whole (W) | Natural numbers plus zero | 0, 1, 2, 3 ... |
| Integers (Z) | Negatives, zero and positives | ...-2, -1, 0, 1, 2 ... |
| Prime | Exactly two factors: 1 and itself | 2, 3, 5, 7, 11, 13 ... |
| Composite | More than two factors | 4, 6, 8, 9, 10, 12 ... |
| Even / Odd | Divisible / not divisible by 2 | Even: 2, 4, 6 · Odd: 1, 3, 5 |
Part 2: Divisibility Rules — your speed weapon
In 90 minutes you have to attempt 100 questions. You simply do not have time to do long division for every number. Divisibility rules let you check in your head whether one number divides another. Master this table and you will save precious minutes on factors, HCF, LCM and simplification questions.
| Divisible by | Rule | Quick check |
|---|---|---|
| 2 | Last digit is even (0, 2, 4, 6, 8) | 3746 ends in 6 |
| 3 | Sum of digits is divisible by 3 | 1242 → 1+2+4+2 = 9 |
| 4 | Last two digits divisible by 4 | 1316 → 16 ÷ 4 = 4 |
| 5 | Ends in 0 or 5 | 2035 ends in 5 |
| 6 | Divisible by BOTH 2 and 3 | 534 → even & digit sum 12 |
| 8 | Last three digits divisible by 8 | 7120 → 120 ÷ 8 = 15 |
| 9 | Sum of digits is divisible by 9 | 8172 → 8+1+7+2 = 18 |
| 10 | Ends in 0 | 4890 ends in 0 |
| 11 | (odd-place sum − even-place sum) = 0 or a multiple of 11 | 1331 → (1+3) − (3+1) = 0 |
Part 3: LCM and HCF
🧠 Bells vs ribbons
HCF (Highest Common Factor) is like cutting three ribbons of different lengths into the LARGEST equal pieces with nothing wasted — you want the biggest common size. LCM (Least Common Multiple) is like three temple bells ringing at different intervals — LCM tells you when they will all ring TOGETHER again for the first time. HCF = biggest common divider, LCM = smallest common meeting point.
📝 Find the LCM and HCF of 12 and 18
Step 1 — Prime factorise: 12 = 2 × 2 × 3 = 2² × 3
18 = 2 × 3 × 3 = 2 × 3²
Step 2 — HCF = product of the LOWEST powers of common primes = 2¹ × 3¹ = 6
Step 3 — LCM = product of the HIGHEST powers of all primes = 2² × 3² = 4 × 9 = 36
Step 4 — Verify with the formula: LCM × HCF = 36 × 6 = 216
Product of numbers = 12 × 18 = 216 ✓
Answer: HCF = 6, LCM = 36
Part 4: BODMAS — the order of operations
Simplification questions look scary but are the easiest marks in the paper IF you follow one rule: BODMAS. It tells you the exact order in which to solve. Break the rule and you will get a clean-looking wrong answer — which is exactly what the distractor options are waiting for.
The BODMAS order
- 1B — Brackets first: solve ( ), then { }, then [ ], from inside to outside.
- 2O — Of / Orders: powers, square roots, and the word 'of' (e.g. 1/2 of 8 = 4).
- 3D and M — Division and Multiplication, done left to right (they have EQUAL priority).
- 4A and S — Addition and Subtraction, done left to right (also equal priority).
📝 Simplify: 36 ÷ 6 + 4 × 3 − (5 + 2)
Step 1 — Brackets: (5 + 2) = 7 → 36 ÷ 6 + 4 × 3 − 7
Step 2 — Division: 36 ÷ 6 = 6 → 6 + 4 × 3 − 7
Step 3 — Multiplication: 4 × 3 = 12 → 6 + 12 − 7
Step 4 — Addition: 6 + 12 = 18 → 18 − 7
Step 5 — Subtraction: 18 − 7 = 11
Answer: 11
60-second revision before the exam
- ✓1 is neither prime nor composite; 2 is the only even prime.
- ✓Divisible by 3 or 9 → add the digits. Divisible by 11 → alternate-place difference.
- ✓Divisible by 6 means divisible by both 2 and 3.
- ✓HCF = biggest common divider (grouping); LCM = smallest common multiple (meeting again).
- ✓LCM × HCF = product of the two numbers.
- ✓BODMAS: Brackets → Of/Orders → Divide & Multiply (left to right) → Add & Subtract (left to right).
⚡ Quick check
Simplify: 8 + 2 × 5
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