Question:
The remainder when \( 7^{84} \) is divided by \( 342 \) is :
The remainder when \( 7^{84} \) is divided by \( 342 \) is :
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Note that \( 7^3 = 343 = 342 + 1 \).
Updated On: Nov 4, 2026
- 1
- 0
- 49
- 341
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Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Use \( 7^3 \).
\( 7^3 = 343 = 342 + 1 \), so \( 7^3 \equiv 1 \pmod{342} \).
Step 2: Write the exponent.
\( 84 = 3 \times 28 \), so \( 7^{84} = (7^3)^{28} \).
Step 3: Reduce.
\( (7^3)^{28} \equiv 1^{28} = 1 \pmod{342} \).
Final Answer:
The correct option is (1): 1
\( 7^3 = 343 = 342 + 1 \), so \( 7^3 \equiv 1 \pmod{342} \).
Step 2: Write the exponent.
\( 84 = 3 \times 28 \), so \( 7^{84} = (7^3)^{28} \).
Step 3: Reduce.
\( (7^3)^{28} \equiv 1^{28} = 1 \pmod{342} \).
Final Answer:
The correct option is (1): 1
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