Number System — The Foundation of All Quant
A concept-first guide to the Number System for SSC-CGL: how numbers are classified, must-know divisibility rules, key sum formulas, the unit-digit (cyclicity) trick with a worked example, and a quiz to test yourself.
By the PadhoDost Team · 📖 7 min read · Updated 4 August 2026
Part of SSC CGL & Banking prep🧠 A family tree of numbers
Think of numbers like a family. The counting numbers 1, 2, 3... are the youngest children (natural numbers). Add zero and they become whole numbers. Bring in the negatives and you have integers. Add all the fractions and you get rational numbers, and finally the odd cousins like the square root of 2 and pi that never settle into a neat fraction — the irrationals. Together the whole family makes up the real numbers.
The Number System is the base of every Quant topic, so knowing exactly which family a number belongs to, and a few quick rules, lets you solve questions in seconds instead of doing long calculations.
| Type | Meaning | Examples |
|---|---|---|
| Natural (N) | Counting numbers from 1 | 1, 2, 3, 4, ... |
| Whole (W) | Naturals together with 0 | 0, 1, 2, 3, ... |
| Integers (Z) | Positives, negatives and zero | ..., -2, -1, 0, 1, 2, ... |
| Rational (Q) | Can be written as p/q, q not 0 | 1/2, -3, 0.75, 4 |
| Irrational | Non-terminating, non-repeating decimals | sqrt(2), pi, sqrt(3) |
| Prime | Exactly two factors: 1 and itself | 2, 3, 5, 7, 11 (2 is the only even prime) |
Divisibility Rules You Must Know
| Divisible by | Quick test |
|---|---|
| 2 | Last digit is even (0,2,4,6,8) |
| 3 | Sum of all digits is divisible by 3 |
| 4 | Number formed by the last two digits is divisible by 4 |
| 5 | Last digit is 0 or 5 |
| 6 | Divisible by both 2 and 3 |
| 8 | Number formed by the last three digits is divisible by 8 |
| 9 | Sum of all digits is divisible by 9 |
| 10 | Ends in 0 |
| 11 | Difference between the sums of alternate digits is 0 or a multiple of 11 |
Key Sum Formulas
Finding the Unit (Last) Digit
The last digit of a power repeats in a short cycle called its cyclicity. For most digits the cycle length is 4, so you just divide the power by 4 and use the remainder to pick the answer. Digits 0, 1, 5 and 6 always keep the same last digit, so they need no cycle.
📝 Worked example — unit digit of 3^47
Powers of 3 end in a repeating cycle: 3, 9, 7, 1 (then it repeats every 4).
Divide the power by 4: 47 divided by 4 = 11 remainder 3.
A remainder of 3 points to the 3rd number in the cycle 3, 9, 7, 1.
The 3rd term is 7.
Answer: the unit digit of 3^47 is 7.
Remember these
- ✓Know the number families: natural, whole, integer, rational, irrational, real.
- ✓2 is the only even prime number; 1 is neither prime nor composite.
- ✓Master the divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10 and 11.
- ✓Sum of first n natural numbers = n(n+1)/2, and sum of first n odd numbers = n^2.
- ✓Use cyclicity (usually a cycle of 4) to find the last digit of large powers.
⚡ Quick check
Which of these numbers is divisible by 9?
Ready to test yourself? 🎯
Lock it in with the practice test for this chapter.
Take the practice test →