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

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GMAT Panda · Accepted Answer

1 We translate the phrase "remainder when 3^24 is divided by 5" into an equation relating the divisor, quotient, and remainder. 5k + r = 3^24 We calculate the remainder when 3^4 is divided by 5, since we will use that to simplify 3^24. 3^4 = 81 = 516 + 1 remainder of 3^4 divided by 5 = 1 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 = (516 + 1)^6 remainder = 1^6 = 1

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$We translate the phrase "remainder when 3^{24} is divided by 5" into an equation relating the divisor, quotient, and remainder.$	$5 k + r = 3^{24}$
$We calculate the remainder when 3^{4} is divided by 5, since we will use that to simplify 3^{24} .$	$3^{4} = 81 = 5 \times 16 + 1 remainder of 3^{4} divided by 5 = 1$
$We express 3^{24} as (3^{4})^{6} and use the remainder of 3^{4} to find the remainder of the entire expression.$	$3^{24} = (3^{4})^{6} = (5 \times 16 + 1)^{6} remainder = 1^{6} = 1$

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