Find the remainder of the division 2100/7.
Explanation:
Let us find the pattern that remainders follow when successive powers of 2 are divided by 7.
Remainder of 21/7 = 2. Remainder of 22/7 = 4. Remainder of 23/7 = 1. Remainder of 24/7 = 2. Remainder of 25/7 = 4. Remainder of 26/7 = 1.
∴ We find that the remainders are repeated after every three powers.
∴ R21007 = R299×217 = R2997×R217 = 1 × 2 = 2
⇒ The remainder is 2.
Hence, 2.
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