SSC Notes / Quantitative Aptitude / Chapter 4
Chapter 4 of 27

Divisibility Rules

Quick divisibility tests for 2 through 19 — essential shortcuts that speed up Number System, HCF-LCM, and Simplification questions alike.

📖 ~11 min read 🔢 SSC Quantitative Aptitude

Introduction

Divisibility rules let you instantly check if a number divides another without doing long division — indispensable for Number System, HCF/LCM, and even Data Interpretation questions where large numbers appear under time pressure.

Divisibility Rules Table (2 to 19)

DivisorRule
2Last digit is even (0, 2, 4, 6, 8)
3Sum of digits is divisible by 3
4Last two digits form a number divisible by 4
5Last digit is 0 or 5
6Divisible by both 2 and 3
7Double the last digit, subtract from the rest; result divisible by 7 (repeat if needed)
8Last three digits form a number divisible by 8
9Sum of digits is divisible by 9
10Last digit is 0
11Difference between sum of digits at odd places and even places is 0 or divisible by 11
12Divisible by both 3 and 4
13Multiply last digit by 4, add to the rest; result divisible by 13 (repeat if needed)
19Multiply last digit by 2, add to the rest; result divisible by 19 (repeat if needed)
Q. Is 3696 divisible by 7?
Last digit = 6, remaining = 369
369 − (6 × 2) = 369 − 12 = 357
Repeat: last digit 7, remaining 35 → 35 − 14 = 21 → divisible by 7
So 3696 is divisible by 7.
Q. Is 90728 divisible by 11?
Digits (right to left, alternating): odd places (8,7,0) sum = 15; even places (2,9) sum = 11
Difference = 15 − 11 = 4 → not divisible by 11
So 90728 is not divisible by 11.

Combining Rules for Composite Divisors

DivisorCheck divisibility by
62 and 3
123 and 4
153 and 5
182 and 9
364 and 9
⚠️ Common Trap: The two divisors you combine must be co-prime (HCF = 1) for this shortcut to work — e.g., you cannot check divisibility by 8 using "divisible by 2 and 4" since 2 and 4 aren't co-prime; use the direct 8-rule instead.

Finding the Missing Digit

Q. Find the value of x if 46x72 is divisible by 9.
Sum of known digits = 4+6+7+2 = 19
Need (19 + x) divisible by 9 → smallest x making it divisible by 9 is x = 8 (19+8=27)
So x = 8
✅ Practice Focus: Memorise all rules from 2-13 and 19 cold · Composite divisor combination trick (must be co-prime) · Missing-digit problems using digit-sum rules (3, 9, 11).

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