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When (3)^1989 is divided by 7 the reminder will be?
Most Upvoted Answer
When (3)^1989 is divided by 7 the reminder will be?
Explanation:
To find the remainder when \(3^{1989}\) is divided by 7, we can use the concept of modular arithmetic.
Modular Arithmetic:
Modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value called the modulus.
Using Fermat's Little Theorem:
Fermat's Little Theorem states that if p is a prime number, then for any integer a not divisible by p, \(a^{p-1} \equiv 1 \pmod p\).
Applying Fermat's Little Theorem:
In this case, the modulus is 7, which is a prime number. Therefore, we can apply Fermat's Little Theorem to simplify the calculation.
\(3^{1989} \equiv 3^{1989 \mod 6} \pmod 7\)
\(1989 \mod 6 = 3\)
\(3^{1989} \equiv 3^3 \equiv 27 \equiv 6 \pmod 7\)
Final Answer:
When \(3^{1989}\) is divided by 7, the remainder is 6.
To find the remainder when \(3^{1989}\) is divided by 7, we can use the concept of modular arithmetic.
Modular Arithmetic:
Modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value called the modulus.
Using Fermat's Little Theorem:
Fermat's Little Theorem states that if p is a prime number, then for any integer a not divisible by p, \(a^{p-1} \equiv 1 \pmod p\).
Applying Fermat's Little Theorem:
In this case, the modulus is 7, which is a prime number. Therefore, we can apply Fermat's Little Theorem to simplify the calculation.
\(3^{1989} \equiv 3^{1989 \mod 6} \pmod 7\)
\(1989 \mod 6 = 3\)
\(3^{1989} \equiv 3^3 \equiv 27 \equiv 6 \pmod 7\)
Final Answer:
When \(3^{1989}\) is divided by 7, the remainder is 6.
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When (3)^1989 is divided by 7 the reminder will be?
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When (3)^1989 is divided by 7 the reminder will be? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about When (3)^1989 is divided by 7 the reminder will be? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When (3)^1989 is divided by 7 the reminder will be?.
When (3)^1989 is divided by 7 the reminder will be? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about When (3)^1989 is divided by 7 the reminder will be? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When (3)^1989 is divided by 7 the reminder will be?.
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