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Quantitative Aptitude

Divisibility Rule for Powers of 2 & 5

The remainder...

Question

The remainder when $3^{37}$ is divided by 80 is

A

78

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B

3

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C

2

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D

35

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Solution

The correct option is B 3
$3^{37} = 3^{4.9} .3 = 3. (81)^{9} = 3 (80 + 1)^{9} = 3 (^{9} C_{0} 80^{9} +^{9} C {1.80}^{8} + . . . . +^{9} C_{9}) T h u s, r e q u i r e d r e m a i n d e r i s e q u a l t o 3$

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