Number System – Quick & Easy Study Notes
(For SSC CGL / CHSL – Quantitative Aptitude)
Goal: Get comfortable with all the basic number ideas you’ll see in the exam.
Style: Plain English, short sentences, everyday analogies, tiny examples.
1. The Numbers You See Every Day
| Type | What It Looks Like | Where You See It |
|---|---|---|
| Natural numbers | 1, 2, 3, … | Counting apples |
| Whole numbers | 0, 1, 2, … | Money in your wallet |
| Integers | …, –3, –2, –1, 0, 1, 2, … | Temperature (°C) |
| Fractions | ½, ⅔, ¾ | A pizza cut into 4 pieces |
| Decimals | 0.5, 2.75, 3.1415… | 2.5 kg of sugar |
| Rational numbers | Any fraction or decimal that can be written as a fraction | 0.25 = ¼ |
| Irrational numbers | 3.1415…, √2 | π, √2 (never end) |
Everyday analogy: Think of numbers as building blocks that can be whole, sliced, or rounded.
2. Adding, Subtracting, Multiplying, Dividing
| Operation | Quick Rule | Tiny Example |
|---|---|---|
| Add | Same place value (units, tens, …) | 23 + 15 = 38 |
| Subtract | Borrow if needed | 50 – 27 = 23 |
| Multiply | Do it in parts (2 × 13 = 2 × 10 + 2 × 3) | 4 × 7 = 28 |
| Divide | Find how many times the divisor fits into the dividend | 21 ÷ 3 = 7 |
Tip: Keep the numbers small until the last step—makes mental math easier.
3. Powers & Roots (Exponents)
| Symbol | Meaning | Tiny Example |
|---|---|---|
x² |
x multiplied by itself | 3² = 3 × 3 = 9 |
x³ |
x × x × x | 2³ = 8 |
√x |
Number that, when squared, gives x | √9 = 3 |
x⁰ |
Any number (except 0) to the power 0 = 1 | 5⁰ = 1 |
Analogy: A power is like “making a stack” of the same number.
Root is the opposite—“what number, when stacked, becomes the given number?”
4. Prime vs. Composite Numbers
| Prime | Composite | Everyday Analogy |
|---|---|---|
| A number >1 that has only 1 and itself as divisors | A number >1 that has at least one divisor other than 1 and itself | Prime: a unique Lego block. Composite: a Lego set made by combining blocks. |
| 2, 3, 5, 7, 11, 13, … | 4, 6, 8, 9, 10, 12, … |
Tiny test: Is 13 prime?
13 ÷ 2 (no), ÷ 3 (no), ÷ 5 (no). → Prime.
5. Factors & Multiples
| Factor | Multiple | Everyday Analogy |
|---|---|---|
| A number that divides another exactly (no remainder) | A number you get when you multiply a given number by any integer | Factor: a toy that fits into the box. Multiple: the box filled with that toy. |
| Example: Factors of 12 are 1, 2, 3, 4, 6, 12 | Multiples of 3 are 3, 6, 9, 12, … |
Rule of thumb: List all numbers that “fit” into the number without cutting it.
6. Greatest Common Divisor (GCD) & Least Common Multiple (LCM)
| GCD | LCM |
|---|---|
| Smallest number that both numbers share as a factor | Smallest number that both numbers can multiply into |
| Example: GCD(8,12) = 4 | Example: LCM(8,12) = 24 |
| How to find (quick): List factors of each, pick the biggest common one. | How to find (quick): List multiples of each, pick the smallest common one. |
Mini‑story: GCD = “common friend” that sits in both groups. LCM = “smallest party” that both groups can attend together.
7. Divisibility Rules – Quick Checks
| Divisible by | Check |
|---|---|
| 2 | Last digit is even (0,2,4,6 |