What is the remainder when 47^203 is divided by 7?

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Official Explanation

Official

It will not be correct to check on units digit when finding remainder on division by 7. Units digit will help while finding remainders on division by 5 and 10.

Here

47^{203}=(49-2)^{203}

. All terms on expansion except

(-2)^{203}

will be divisible by 7.

(-2)^{203} = (-2)^{202}*(-2) = (2)^{202}*(-2) = (2^3)^{67}*2*(-2) = (8)^{67}*2*(-2) = (7+1)^{67}*2*(-2) = 1^{67}*(-4) = -4

…

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What this question tests

What it tests

Your understanding of divisibility rules, least common multiples, and greatest common factors.

Common trap

Forgetting that 1 is not prime and that every integer divides 0.