Unit Digit Tricks for SSC CGL (Quick Answer)
The fastest unit digit trick for SSC CGL is the cyclicity rule: the last digit of any power depends only on the last digit of the base and on the remainder when the power is divided by 4. Digits 0, 1, 5 and 6 never change, 4 and 9 repeat every 2 powers, and 2, 3, 7 and 8 repeat every 4 powers. For products, sums and differences you simply combine the unit digits of each part.
🔥 Key Exam Takeaway: Divide the power by 4. If the remainder is 1, 2 or 3, use that power of the last digit. If the remainder is 0, use the 4th power. Example: 7⁹⁵ → 95 ÷ 4 leaves 3 → 7³ = 343 → unit digit 3.
Unit digit questions come up in the Number System part of SSC CGL, CHSL, MTS and CPO quant and occasionally in bank prelims. Every answer in this note has been checked by direct computation.
Unit Digit Cyclicity Table (0 to 9)
| Last digit of base | Unit digits of powers 1, 2, 3, 4 | Cycle length | Rule |
|---|---|---|---|
| 0 | 0 | 1 | Always 0 |
| 1 | 1 | 1 | Always 1 |
| 2 | 2, 4, 8, 6 | 4 | Use remainder of power ÷ 4 |
| 3 | 3, 9, 7, 1 | 4 | Use remainder of power ÷ 4 |
| 4 | 4, 6 | 2 | Odd power → 4, even power → 6 |
| 5 | 5 | 1 | Always 5 |
| 6 | 6 | 1 | Always 6 |
| 7 | 7, 9, 3, 1 | 4 | Use remainder of power ÷ 4 |
| 8 | 8, 4, 2, 6 | 4 | Use remainder of power ÷ 4 |
| 9 | 9, 1 | 2 | Odd power → 9, even power → 1 |
Memory hooks:
- 2 and 8 are mirror images: 2 → 2, 4, 8, 6 and 8 → 8, 4, 2, 6.
- 3 and 7 are mirror images: 3 → 3, 9, 7, 1 and 7 → 7, 9, 3, 1.
- When the power is a multiple of 4, the unit digit is 6 for 2, 4, 6, 8 (even digits) and 1 for 3, 7, 9 (odd digits other than 5).
How to Find the Unit Digit of a Number with Power
To find the unit digit of aⁿ:
- Keep only the last digit of the base. The unit digit of 3127¹⁷³ is the same as that of 7¹⁷³.
- Check the digit type. If it is 0, 1, 5 or 6, the answer is that digit. If it is 4 or 9, check whether n is odd or even.
- For 2, 3, 7, 8, find n ÷ 4. You only need the last two digits of n to find this remainder, because 100 is divisible by 4.
- Use the remainder. Remainder 1, 2 or 3 → raise the last digit to that power. Remainder 0 → raise it to the 4th power.
- Read the last digit of that small result.
| Remainder of n ÷ 4 | Use | Last digit 2 | Last digit 3 | Last digit 7 | Last digit 8 |
|---|---|---|---|---|---|
| 1 | 1st power | 2 | 3 | 7 | 8 |
| 2 | 2nd power | 4 | 9 | 9 | 4 |
| 3 | 3rd power | 8 | 7 | 3 | 2 |
| 0 | 4th power | 6 | 1 | 1 | 6 |
Unit Digit Formula for Products, Sums and Differences
| Operation | Rule | Example |
|---|---|---|
| Product | Multiply the unit digits, keep the last digit | Unit digit of 23 × 47 × 59: 3 × 7 × 9 = 189 → 9 |
| Sum | Add the unit digits, keep the last digit | 7² + 3² → 9 + 9 = 18 → 8 |
| Difference | Subtract the unit digits; if negative, add 10 | 3 − 7 = −4 → −4 + 10 = 6 |
| Any factor ending in 5 × any even number | Unit digit is 0 | 15 × 22 → 0 |
| Factor ending in 5 × only odd numbers | Unit digit is 5 | 5 × 7 × 9 → 5 |
| Factor ending in 0 | Unit digit is 0 | 120 × 37 → 0 |
Unit Digit of Factorials (Sum of Factorials Trick)
- For n ≥ 5, n! contains both 2 and 5, so the unit digit of n! is 0.
- 1! = 1, 2! = 2, 3! = 6, 4! = 24.
- Sum 1! + 2! + 3! + … + n! for any n ≥ 4: only the first four terms matter. 1 + 2 + 6 + 24 = 33, so the unit digit is 3.
- For n = 1, 2, 3 the sum's unit digit is 1, 3 and 9 respectively.
- Product of factorials 1! × 2! × 3! × 4! = 1 × 2 × 6 × 24 = 288 → unit digit 8. Once 5! is included, the unit digit becomes 0.
Unit Digit Questions with Solutions (SSC CGL and CHSL Style)
Example 1: Basic power
Find the unit digit of 7⁹⁵.
Solution: 95 ÷ 4 leaves remainder 3. 7³ = 343. Answer: 3.
Example 2: Year-style power
Find the unit digit of 2²⁰²⁶.
Solution: Last two digits of the power are 26; 26 ÷ 4 leaves remainder 2. 2² = 4. Answer: 4.
Example 3: Large base
Find the unit digit of (3127)¹⁷³.
Solution: Base ends in 7. 73 ÷ 4 leaves remainder 1, so use 7¹. Answer: 7.
Example 4: Remainder zero
Find the unit digit of (2137)⁷⁵⁶.
Solution: Base ends in 7. 56 ÷ 4 leaves remainder 0, so use 7⁴ = 2401. Answer: 1.
Example 5: Product of powers (SSC CGL Tier 1 pattern)
Find the unit digit of 3⁶⁵ × 6⁵⁹ × 7⁷¹.
Solution:
- 3⁶⁵: 65 ÷ 4 leaves 1 → 3
- 6⁵⁹ → 6
- 7⁷¹: 71 ÷ 4 leaves 3 → 3
- Product of unit digits: 3 × 6 × 3 = 54
Answer: 4.
Example 6: Digits 4 and 9
Find the unit digits of 4⁹⁹, 4¹⁰⁰, 9²⁰²⁵ and 9²⁰²⁶.
Solution: 4 with an odd power → 4, even power → 6. 9 with an odd power → 9, even power → 1. Answers: 4, 6, 9, 1.
Example 7: Sum of powers
Find the unit digit of (1739)²⁰²⁶ + (2341)⁷.
Solution: 9 with an even power → 1. Base ending in 1 → 1. Sum 1 + 1 = 2. Answer: 2.
Example 8: Difference that goes negative
Find the unit digit of 17⁸³ − 13⁸³.
Solution: 83 ÷ 4 leaves 3. 7³ ends in 3 and 3³ ends in 7. 3 − 7 = −4, add 10 → 6. Answer: 6. (The number itself is positive, since 17⁸³ > 13⁸³.)
Example 9: Difference with equal cycles
Find the unit digit of 7⁸⁴ − 3⁸⁴.
Solution: 84 is a multiple of 4, so both end in 1. 1 − 1 = 0. Answer: 0.
Example 10: Mixed product
Find the unit digit of 13⁷⁵ × 14⁴².
Solution: 13⁷⁵: 75 ÷ 4 leaves 3 → 3³ = 27 → 7. 14⁴²: 4 with an even power → 6. 7 × 6 = 42. Answer: 2.
Example 11: Power tower
Find the unit digit of 7 raised to the power 7⁷.
Solution: We need 7⁷ ÷ 4. Since 7 leaves remainder 3 when divided by 4, and 3 raised to an odd power leaves remainder 3 when divided by 4, 7⁷ leaves remainder 3. So use 7³ = 343. Answer: 3.
Example 12: Sum of factorials
Find the unit digit of 1! + 2! + 3! + … + 50!.
Solution: From 5! onwards every term ends in 0. 1 + 2 + 6 + 24 = 33. Answer: 3.
Example 13: Product of odd numbers
Find the unit digit of 1 × 3 × 5 × 7 × … × 99.
Solution: The product contains 5 and no even number, so the unit digit is 5. Answer: 5.
Example 14: Powers that share a base
Find the unit digit of (264)¹⁰² + (264)¹⁰³.
Solution: 4 with an even power → 6, with an odd power → 4. 6 + 4 = 10. Answer: 0.
Example 15: Subtraction with different bases
Find the unit digit of 12⁵⁵ − 8³⁰.
Solution: 12⁵⁵: 55 ÷ 4 leaves 3 → 2³ = 8. 8³⁰: 30 ÷ 4 leaves 2 → 8² = 64 → 4. 8 − 4 = 4. Answer: 4.
Common Mistakes in Unit Digit Questions
- Remainder 0 does not mean digit 0. When the power is a multiple of 4, use the 4th power (6 for 2 and 8, 1 for 3 and 7).
- Using the whole power instead of the remainder. You never need 7⁹⁵ itself. Only 95 ÷ 4 matters.
- Using the whole base. Only the last digit of the base matters: 3127 behaves like 7.
- Negative result in subtraction. If the unit digit of the first term is smaller, add 10 to the difference (3 − 7 → 6, not 4).
- Forgetting that 5 × even = 0. A single factor ending in 5 and any even factor make the unit digit 0.
- Treating 4 and 9 as 4-cycle digits. They repeat every 2 powers, so only odd or even matters.
- Counting factorial terms beyond 4!. In 1! + 2! + … + n!, everything from 5! onwards adds 0 to the unit digit.
Unit Digit Short Tricks: Quick Revision Table
| Question type | Shortcut | Result |
|---|---|---|
| 0, 1, 5, 6 to any power | No change | Same digit |
| 4ⁿ | Odd/even | 4 / 6 |
| 9ⁿ | Odd/even | 9 / 1 |
| 2, 3, 7, 8 to the power n | n ÷ 4 (use last two digits of n) | See cycle; remainder 0 → 4th power |
| Product | Multiply unit digits | Last digit of product |
| Sum / difference | Add / subtract unit digits | Add 10 if negative |
| n! (n ≥ 5) | Has 2 × 5 | 0 |
| 1! + 2! + … + n! (n ≥ 4) | Only first four terms | 3 |
| Product with 5 and an even number | 2 × 5 = 10 | 0 |
| Sum of 4 consecutive powers of 2, 3, 7 or 8 | One full cycle adds to 20 | 0 |
Unit Digit Practice Questions for SSC CGL with Answers
Q1. Find the unit digit of 8⁴⁷. Answer: 2. 47 ÷ 4 leaves 3; 8³ = 512.
Q2. Find the unit digit of (379)⁶⁴. Answer: 1. Base ends in 9 and the power is even.
Q3. Find the unit digit of 2⁸⁵ × 3⁴². Answer: 8. 2⁸⁵: remainder 1 → 2. 3⁴²: remainder 2 → 9. 2 × 9 = 18.
Q4. Find the unit digit of (122)¹⁷³. Answer: 2. Base ends in 2; 73 ÷ 4 leaves 1 → 2.
Q5. Find the unit digit of 1! + 2! + 3! + … + 100!. Answer: 3. Only 1 + 2 + 6 + 24 = 33 matters.
Q6. Find the unit digit of 4¹³¹ × 9⁷⁹. Answer: 6. Odd powers: 4 and 9. 4 × 9 = 36.
Q7. Find the unit digit of 5²⁰²⁶ + 6²⁰²⁶. Answer: 1. 5 + 6 = 11.
Q8. Find the unit digit of 3 raised to the power 3³ (that is, 3²⁷). Answer: 7. 27 ÷ 4 leaves 3; 3³ = 27.
Q9. Find the unit digit of 51 × 52 × 53 × … × 60. Answer: 0. The product contains 55 and even numbers (and also 60).
Q10. Find the unit digit of 3¹ + 3² + 3³ + … + 3²⁰. Answer: 0. Each block of four powers ends in 3 + 9 + 7 + 1 = 20, i.e. 0. There are 5 such blocks.
Q11. Find the unit digit of 7³⁵ × 3⁷¹ × 11⁵⁵. Answer: 1. 7³⁵: remainder 3 → 3. 3⁷¹: remainder 3 → 7. 11⁵⁵ → 1. 3 × 7 × 1 = 21.
Q12. Find the unit digit of 1! × 2! × 3! × 4!. Answer: 8. 1 × 2 × 6 × 24 = 288.
Unit Digit Tricks FAQs
What is cyclicity in unit digit questions?
Cyclicity is the number of powers after which the unit digit repeats. It is 1 for 0, 1, 5, 6; 2 for 4 and 9; and 4 for 2, 3, 7 and 8.
How do you find the unit digit of a large power quickly?
Keep the last digit of the base, divide the power by 4 (using its last two digits), and use the remainder as the new power. If the remainder is 0, use 4.
What is the unit digit when the power is divisible by 4?
For bases ending in 2, 4, 6 or 8 it is 6. For bases ending in 3, 7 or 9 it is 1. Bases ending in 0, 1 and 5 keep their own digit.
What is the unit digit of 1! + 2! + 3! + … + 100!?
It is 3, because every factorial from 5! onwards ends in 0 and 1 + 2 + 6 + 24 = 33.
How do you find the unit digit of a difference like 17⁸³ − 13⁸³?
Find each unit digit (3 and 7), subtract, and add 10 if the result is negative. Here 3 − 7 = −4, so the answer is 6.
Is the unit digit topic asked in SSC CGL?
Yes. It is part of the Number System chapter in SSC CGL and CHSL quant, usually as a one-mark question on powers, products or factorial sums.
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