1
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Question

# The remainder when 32(32)(32) is divided by 7, is

A
1
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B
2
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C
3
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D
4
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Solution

## The correct option is D 4The option d is correct.Rem[323232/7]=Rem[43232/7]Now, we need to observe the pattern41 when divided by 7, leaves a remainder of 442 when divided by 7, leaves a remainder of 243 when divided by 7, leaves a remainder of 1And then the same cycle of 4,2, and 1 will continue.If a number is of the format of 4(3k+1), it will leave a remainder of 4If a number is of the format of 4(3k+2), it will leave a remainder of 2If a number is of the format of 4(3k), it will leave a remainder of 1The number given to us is 43232Let us find out Rem[Power / Cyclicity] to find out if it 4(3k+1) or4(3k+2). We can just look at it and say that it is not 43kRem[3232/3]=Rem[(−1)32/3]=1=> The number is of the format 4(3k+1)=> Rem[43232/7]=4

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