Question:
What is the remainder when \(7^{100}\) is divided by 5?
What is the remainder when \(7^{100}\) is divided by 5?
Show Hint
Track the remainders of successive powers of 7 when divided by 5 directly, and look for when the pattern starts repeating.
Updated On: Jul 8, 2026
- 4
- 1
- 2
- 3
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The Correct Option is B
Solution and Explanation
\(7\equiv 2\pmod 5\), so \(7^{100}\equiv 2^{100}\pmod 5\). Since \(2^4=16\equiv 1\pmod 5\) and \(100=4\times 25\), \(2^{100}=(2^4)^{25}\equiv 1^{25}=1\pmod 5\). Remainder \(=1\). Correct option: 1.
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