What is the remainder when 333^222 is divided… | GMAT Sprint

Free Practice Question

PS · Problem Solving

705-805

Divisibility/Multiples/Factors

What is the remainder when $333^{222}$ is divided by 7?

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Official Explanation

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What is the remainder when

333^{222}

is divided by 7?

333^{222} = (329+4)^{222} = (7 \times 47 + 4)^{222}

.

Now, if we expand this, all terms but the last one will have

7 \times 47

as a multiple and thus will be divisible by 7. The last term will be

4^{222} = 2^{444}

.

So we should find the remainder when

2^{444}

is divided by 7.

2^1

divided by 7 yields remainder of 2;

2^2

divided by 7 yields remainder of 4;

2^3

divided by 7 yields remainder of 1;

2^4

divided by 7 yields remainder of 2;

2^5

divided by 7 yields remainder of 4;

2^6

divided by 7 yields remainder of 1;…

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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.

What is the remainder when 333222333^{222}333222 is divided by 7?