Aspire Faculty ID #17247 · Topic: CUET UG 2022 Applied Mathematics · Just now
CUET UG 2022 Applied Mathematics

The number at unit place of number $17^{123}$ is:

Solution

Unit digit depends on $7^{123}$

Cycle of unit digits of powers of 7:

$7^1=7$
$7^2=49$ → 9
$7^3=343$ → 3
$7^4=2401$ → 1

Cycle repeats every 4.

Now,

$123 \mod 4$

$123=4\times 30+3$

Remainder = 3

So unit digit same as $7^3$

Unit digit = 3
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