What is the remainder when 2¹⁰ is divided by 7?

2. Remainders of powers of 2 on division by 7 repeat 2, 4, 1. 10 = 3 × 3 + 1, so 2¹⁰ leaves the same as 2¹, which is 2. Check: 1024 = 7 × 146 + 2.

What is the remainder when $2^{10}$ is divided by 7?

Class 8Parity, Remainders and Digital RootsNumber System

Remainders of powers of 2 on division by 7 repeat 2, 4, 1.

10 = 3 \times 3 + 1

, so

2^{10}

leaves the same as

2^{1}

, which is 2. Check:

1024 = 7 \times 146 + 2

Answer: D) 2

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