GMAT Remainder Explained — Remainder when 3^{24} is divided by 5 ?

What is the remainder when 3^{24} is divided by 5 ?

remaindersexponentsnumber theory

Explanation	Calculations	Help
$We translate the phrase $\textbf{"remainder when 3^{24} is divided by 5"}$ into an equation relating the divisor, quotient, and remainder.$	$5 k + r = 3^{24}$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We calculate the remainder when 3^{4} is divided by 5, since we will use that to simplify 3^{24} .$	$3^{4} = 81 = 5 \times 16 + 1 remainder of 3^{4} divided by 5 = 1$	Theory & Tactics Method Card DIV4-D Click to view full details
$We express 3^{24} as (3^{4})^{6} and use the remainder of 3^{4} to find the remainder of the entire expression.$	$3^{24} = (3^{4})^{6} = (5 \times 16 + 1)^{6} remainder = 1^{6} = 1$	Theory & Tactics Method Card DIV4-D Click to view full details

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