Unit Digit Concept – Number Systems | General Aptitude for GATE

The Unit Digit Concept is one of the most important and frequently asked topics in General Aptitude and Number Systems. It helps you quickly find the last digit of large powers and calculations without solving the entire expression.

What is Unit Digit?

The unit digit of a number is the digit in the ones place.

Example:

• Unit digit of 456 is 6
• Unit digit of 7892 is 2

Why is Unit Digit Important?

• Helps solve questions quickly in exams like GATE, SSC, Banking
• Avoids lengthy calculations
• Saves time in aptitude section

Unit Digit of Powers

To find the unit digit of powers like 2ⁿ, 3ⁿ, 7ⁿ, we observe repeating patterns (cycles).

Important Cycles

How to Find Unit Digit?

Step 1: Identify the last digit of the base number
Step 2: Find the cycle length
Step 3: Divide the power by cycle length
Step 4: Use remainder to find the unit digit

Examples

Example 1: Find unit digit of 2¹⁰

Cycle of 2 → (2, 4, 8, 6) → length = 4
10 ÷ 4 → remainder = 2
So, unit digit = 4

Example 2: Find unit digit of 7²⁰²

Cycle of 7 → (7, 9, 3, 1) → length = 4
202 ÷ 4 → remainder = 2
Unit digit = 9

Example 3: Find unit digit of 9¹⁵

Cycle of 9 → (9, 1) → length = 2
15 ÷ 2 → remainder = 1
Unit digit = 9

Special Cases

• If number ends with 0 → Unit digit = 0
• If number ends with 1 → Unit digit = 1
• If number ends with 5 → Unit digit = 5
• If number ends with 6 → Unit digit = 6

Shortcut Tips

• Always focus only on last digit
• Memorize cycles of 2, 3, 7, 8
• For large powers, use modulus (remainder)

Practice Question

Find the unit digit of 3⁴⁵

Try yourself using the cycle method!

Conclusion

The unit digit concept is a powerful shortcut in General Aptitude. By understanding patterns and cycles, you can solve complex problems in seconds. This topic is highly important for exams like GATE, SSC, Banking, and other competitive exams.

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