Question
The unit's digit of \((1373)^{36} - (1442)^{20}\) is:
This question was previously asked in
RRB ALP 2018 CBT 2 Fitter Question Paper (21-Jan-2019) (Shift 3)
The correct answer is
5
Unit Digit Calculation for Powers
To find the unit digit of large powers, we examine the cyclicity of the unit digits of the base.
Unit Digit of (1373)36
- The unit digit of the base is 3.
- The cycle of unit digits for powers of 3 is: 3, 9, 7, 1. The cycle length is 4.
- We need to find the remainder when the exponent (36) is divided by the cycle length (4).
- Calculation: \(36 \div 4 = 9\) with a remainder of \(0\).
- A remainder of \(0\) corresponds to the last digit in the cycle (the 4th digit).
- Therefore, the unit digit of (1373)36 is 1.
Unit Digit of (1442)20
- The unit digit of the base is 2.
- The cycle of unit digits for powers of 2 is: 2, 4, 8, 6. The cycle length is 4.
- We need to find the remainder when the exponent (20) is divided by the cycle length (4).
- Calculation: \(20 \div 4 = 5\) with a remainder of \(0\).
- A remainder of \(0\) corresponds to the last digit in the cycle (the 4th digit).
- Therefore, the unit digit of (1442)20 is 6.
Difference Unit Digit Calculation
We need to find the unit digit of the expression (1373)36 - (1442)20.
- Unit digit of (1373)36 is 1.
- Unit digit of (1442)20 is 6.
- We need the unit digit of (Unit Digit of First Term) - (Unit Digit of Second Term).
- This is the unit digit of \(1 - 6\).
- Since \(1\) is less than \(6\), we borrow from the tens place, making it \(11 - 6\).
- Calculation: \(11 - 6 = 5\).
- The unit digit of the given expression is 5.
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Important Questions from Unit Digit
The unit digit in 4 × 38 × 764 × 1256 is:
How many times does the number 3 occur in unit's place for numbers ranging from 1 to 100?
A. 20
B. 11
C. 10
D. 19
Find the unit digit in the given factor (3451) 51 × (531) 43 .
A. 6
B. 4
C. 1
D. 9
What is the unit digit of 178 × 593 + 157?
Find the unit digit of $(123)^{123} \times (347)^{347} \times (568)^{568}$.
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