Discussion
What is the remainder when \( 3^{7} \) is divided by \( 8 \)?
Answer: C
Rather than computing the power in full, reduce the base first. Since \( 3^{2} = 9 \equiv 1 \pmod 8 \), every even power of 3 is 1 modulo 8:
\[ 3^{7} = \left(3^{2}\right)^{3} \cdot 3 \equiv 1^{3} \cdot 3 \equiv 3 \pmod 8 \]
The direct route agrees: \( 3^{7} = 2187 \) and \( 2187 = 8 \times 273 + 3 \).
Spotting that the base squares to 1 is what makes this quick, and the same trick handles any power of 3 modulo 8: odd powers leave 3, even powers leave 1.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development