Number System

5 min

Master foundation, divisibility rules, and unit digits for exams.

The Golden Rule

Mastering the Number System requires a strong grip on natural numbers, divisibility rules, and unit digits. Quick identification of prime numbers and divisibility saves precious time in SSC and Railway exams. Always simplify complex powers using cyclic patterns for unit digit questions.

Exam Importance

Forms 10-15% of total questions in SSC CGL, CHSL, and Railway NTPC.
Direct divisibility and unit digit questions take under 30 seconds to solve.
Strong number system basics eliminate calculation errors in arithmetic topics.

Quick Memory Hooks

Even sum for Divisibility by 3 and 9: Sum of digits must be divisible by 3 or 9.
Alternating sum for 11: Difference of sum of odd and even placed digits is 0 or multiple of 11.
Power Cycles for Unit Digit: Powers repeat their unit digit in cycles of 4.

Divisibility Rules (2 to 11)

Divisor	Condition	Example
2, 4, 8	Last 1, 2, 3 digits divisible	104 (by 4)
3, 9	Sum of digits divisible	729 (by 9)
5, 10	Last digit is 0/5 or 0	250 (by 10)
11	Diff of odd/even pos is 0/11	1331 (by 11)

Key Concepts Visualized

Natural

(Counting numbers start 1)

Counting numbers start 1

N = {1, 2, 3, ...}

Whole

(Natural plus zero)

Natural plus zero

W = {0, 1, 2, 3, ...}

Prime

(Divisible by 1 & self)

Divisible by 1 & self

2 is the only even prime.

Unit Digit

(Cyclic power rule)

Cyclic power rule

Divide power by 4.

Common Exam Traps

1 is a prime number1 is neither prime nor composite

A prime number must have exactly two distinct positive divisors.

All negative integers are whole numbersWhole numbers start from 0 onwards

Whole numbers include zero and all positive integers only.

Unit digit of 4^n is always 4Unit digit alternates 4 and 6

4^odd is 4, while 4^even is 6.

Test Your Knowledge

Q1.What is the unit digit of the expression 7^105 × 3^65?

Q2.If the number 54321_7 is divisible by 9, what is the missing digit?

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