Example 1 · level 1
What is the unit digit of 14^299?
- 3
- 7
- 0
- 4
Show solution
- 14 ends in 4; 299 ÷ 4 leaves remainder 3, so use power 3: 4^3 ends in 4.
Answer: 4
SSC & BANK EXAMS: QUANTITATIVE APTITUDE · NUMBER SYSTEM
Unit digit of large powers
Unit digits repeat in cycles of 4. Divide the power by 4 and use the remainder (remainder 0 → use 4).
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Worked examples
Example 2 · level 2
What is the unit digit of 7^281 × 14^115?
- 1
- 4
- 8
- 7
Show solution
- 7 ends in 7; 281 ÷ 4 leaves remainder 1, so use power 1: 7^1 ends in 7.
- 14 ends in 4; 115 ÷ 4 leaves remainder 3, so use power 3: 4^3 ends in 4.
- 7 × 4 = 28 → unit digit 8.
Answer: 8
Example 3 · level 3
What is the unit digit of 37^130 + 2^75?
- 3
- 0
- 6
- 7
Show solution
- 37 ends in 7; 130 ÷ 4 leaves remainder 2, so use power 2: 7^2 ends in 9.
- 2 ends in 2; 75 ÷ 4 leaves remainder 3, so use power 3: 2^3 ends in 8.
- 9 + 8 → unit digit 7.
Answer: 7