Unit Digit Concept for Competitive Exams | Cyclicity Tricks and Solved Examples

Q1. What is unit digit of a number?

The unit digit of a number is the last digit of that number — the digit in the ones place. For example in the number 87963, the unit digit is 3. The unit digit of any calculation depends only on the unit digits of the participating numbers and not on the full numbers. This property is based on the fundamental concept of modular arithmetic and makes unit digit problems very fast to solve using shortcut cyclicity methods without any lengthy calculation.

Q2. How do you find unit digit of addition and multiplication?

To find unit digit of addition, simply add the unit digits of all numbers and take the unit digit of the result. To find unit digit of multiplication, multiply only the unit digits of all numbers step by step taking the unit digit at each step and ignoring all other digits. You never need to calculate the full number — only the unit digits of participating numbers matter in both cases. This concept is closely related to divisibility rules and remainder theorem.

Q3. What is cyclicity method for finding unit digit of powers?

The cyclicity method is based on the fact that unit digits of powers of any number repeat in a fixed cycle of 4. To find unit digit of any number raised to a power, divide the power by 4 and check the remainder. If remainder is 1 the unit digit equals unit digit of base to power 1. If remainder is 2 use unit digit of base squared. If remainder is 3 use unit digit of base cubed. If remainder is 0 use unit digit of base to power 4. This method uses the same division logic covered in our Remainder Theorem concept page.

Q4. What are the special cases in unit digit of powers?

There are important special cases in unit digit of powers. If unit digit of base is 0 the result always ends in 0. If unit digit of base is 1 the result always ends in 1. If unit digit of base is 5 the result always ends in 5. If unit digit of base is 6 the result always ends in 6. For base ending in 4 the unit digit alternates between 4 for odd powers and 6 for even powers. For base ending in 9 the unit digit alternates between 9 for odd powers and 1 for even powers. These patterns are directly related to Power Indices and Surds concepts.

Q5. How do you find last two digits of a number ending in 1?

For any number ending in 1 raised to a power, the last two digits follow a simple property. The unit digit of the result is always 1. The tens digit of the result equals the unit digit of the product of the tens digit of the base and the power. For example to find last two digits of 31 raised to power 8, tens digit = unit digit of 3 multiplied by 8 = unit digit of 24 = 4. So last two digits are 41. Understanding Factors concept and Divisibility rules helps in solving these problems faster.

Q6. Which competitive exams ask unit digit questions?

Unit digit questions are asked in SSC CGL, SSC CHSL, Bank PO, Bank Clerk, Railway RRB, UPSC CSAT, CAT, MAT and all major Indian competitive exams. This topic is also important in AMCAT, eLitmus, TCS NQT and all campus placement aptitude tests. Questions on unit digit of large powers are particularly common in SSC CGL and Railway RRB exams where number theory topics carry high weightage. This topic is also asked in international exams like GMAT and GRE under number properties section.

Q7. What is the cyclicity of unit digit for digit 2?

For any number ending in 2, the unit digits of successive powers follow the cycle 2, 4, 8, 6 repeating every 4 powers. So divide the power by 4 to find remainder. If remainder is 1 unit digit is 2. If remainder is 2 unit digit is 4. If remainder is 3 unit digit is 8. If remainder is 0 unit digit is 6. The same cycle 2, 4, 8, 6 applies to any base number whose unit digit is 2 regardless of the size of the number. This is closely connected to the concept of Number of Zeroes and Remainder Theorem.

Q8. How can I practice unit digit questions for competitive exams?

After understanding the concept and cyclicity rules you can practice on our Exercise on Unit Digit page which contains a large number of solved practice questions covering all types of unit digit problems asked in SSC CGL, Bank PO, Railway RRB, AMCAT, eLitmus and TCS NQT exams. You may also want to study the related topics of Remainder Theorem, Divisibility and Factors to strengthen your number theory preparation. All questions come with detailed step by step solutions and everything is completely free with no registration required.