What is the unit digit of (217) 413 × (819) 547 × (414) 624 × (342) 812 ?
8
Only unit digits of the bases matter, with cyclicities: 2 (cycle 4: 2,4,8,6), 4 (cycle 2: 4,6), 7 (cycle 4: 7,9,3,1), 9 (cycle 2: 9,1).
\(7^{413}\): \(413\bmod 4=1\Rightarrow 7\). \(9^{547}\): odd \(\Rightarrow 9\). \(4^{624}\): even \(\Rightarrow 6\). \(2^{812}\): \(812\bmod 4=0\Rightarrow 6\).
Unit digit of product \(=7\times 9\times 6\times 6 \equiv 3\times 6\times 6 \equiv 8\times 6 \equiv \mathbf{8}\).
Similar Questions
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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
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What is the unit digit of 178 × 593 + 157?
Find the unit digit of $(123)^{123} \times (347)^{347} \times (568)^{568}$.
