Example 1
What is the unit digit of 13^38?
Answer: C) 9
Unit digits of powers of 3 repeat every 4: 3, 9, 7, 1. 38 ÷ 4 leaves remainder 2, so take place 2 of the cycle: 9.
Number System (Unit Digit) questions for competitive exams: rules, worked examples and practice
Number system questions test divisibility, remainders and unit digits. Unit digits of powers repeat in a cycle of at most 4.
Key rules and formulas
- Unit digit of a^n depends only on the unit digit of a and on n mod 4.
- Digits 0, 1, 5 and 6 keep the same unit digit at every power.
- Cycles: 2 → 2,4,8,6; 3 → 3,9,7,1; 7 → 7,9,3,1; 8 → 8,4,2,6; 4 → 4,6; 9 → 9,1.
- If n mod 4 = 0, use the 4th term of the cycle.
Common traps
- Using n mod 4 = 0 as the first term of the cycle.
- Working with the whole number instead of its last digit.
Where Number System (Unit Digit) is asked
- RRB Group D (Mathematics)
- RRB NTPC CBT 1 (Mathematics)
- SSC CGL Tier 1 (Quantitative Aptitude)
- SSC CGL Tier 2 (Mathematical Abilities)
- SSC CHSL Tier 1 (Quantitative Aptitude)
Worked examples
Example 2
What is the unit digit of 7^88?
Answer: C) 1
Unit digits of powers of 7 repeat every 4: 7, 9, 3, 1. 88 ÷ 4 leaves remainder 0, so take place 4 of the cycle: 1.
Example 3
What is the unit digit of 8^25?
Answer: A) 8
Unit digits of powers of 8 repeat every 4: 8, 4, 2, 6. 25 ÷ 4 leaves remainder 1, so take place 1 of the cycle: 8.
Frequently asked questions
What is Number System (Unit Digit) in competitive exams?
Number system questions test divisibility, remainders and unit digits. Unit digits of powers repeat in a cycle of at most 4.
Which exams ask Number System (Unit Digit) questions?
On MockBazaar, Number System (Unit Digit) questions appear in RRB Group D, RRB NTPC CBT 1, SSC CGL Tier 1, SSC CGL Tier 2, SSC CHSL Tier 1.
What is the most common mistake in Number System (Unit Digit)?
Using n mod 4 = 0 as the first term of the cycle.