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A number when divided by 837 leaves a remainder of 79. what will be the remainder when the same number is divided by 31? answer is 17, please explain.?
Most Upvoted Answer
A number when divided by 837 leaves a remainder of 79. what will be th...
Solution:
To find the remainder when a number is divided by 31, we need to use the concept of modular arithmetic.
Step 1: Write the given information using modular arithmetic notation.
Let the number be x. Then, we can write:
x ≡ 79 (mod 837)
This means that x leaves a remainder of 79 when divided by 837.
Step 2: Simplify the given equation.
To simplify the equation, we need to subtract 79 from both sides:
x - 79 ≡ 0 (mod 837)
Step 3: Use the Chinese Remainder Theorem to simplify the equation further.
The Chinese Remainder Theorem states that if we have a system of linear congruences of the form:
x ≡ a (mod m)
x ≡ b (mod n)
where m and n are relatively prime, then the solution can be written as:
x ≡ (an * b * nm) + (bm * a * mn) (mod mn)
In our case, we have:
x - 79 ≡ 0 (mod 837)
x ≡ 0 (mod 31)
Since 837 and 31 are relatively prime, we can use the Chinese Remainder Theorem to simplify the equation:
x ≡ (0 * 31 * 28) + (837 * 79 * 1) ≡ 26173 (mod 26127)
Step 4: Find the remainder when x is divided by 31.
To find the remainder when x is divided by 31, we need to take the remainder of 26173 when divided by 31:
26173 ≡ 17 (mod 31)
Therefore, the remainder when the number is divided by 31 is 17.
To find the remainder when a number is divided by 31, we need to use the concept of modular arithmetic.
Step 1: Write the given information using modular arithmetic notation.
Let the number be x. Then, we can write:
x ≡ 79 (mod 837)
This means that x leaves a remainder of 79 when divided by 837.
Step 2: Simplify the given equation.
To simplify the equation, we need to subtract 79 from both sides:
x - 79 ≡ 0 (mod 837)
Step 3: Use the Chinese Remainder Theorem to simplify the equation further.
The Chinese Remainder Theorem states that if we have a system of linear congruences of the form:
x ≡ a (mod m)
x ≡ b (mod n)
where m and n are relatively prime, then the solution can be written as:
x ≡ (an * b * nm) + (bm * a * mn) (mod mn)
In our case, we have:
x - 79 ≡ 0 (mod 837)
x ≡ 0 (mod 31)
Since 837 and 31 are relatively prime, we can use the Chinese Remainder Theorem to simplify the equation:
x ≡ (0 * 31 * 28) + (837 * 79 * 1) ≡ 26173 (mod 26127)
Step 4: Find the remainder when x is divided by 31.
To find the remainder when x is divided by 31, we need to take the remainder of 26173 when divided by 31:
26173 ≡ 17 (mod 31)
Therefore, the remainder when the number is divided by 31 is 17.
Community Answer
A number when divided by 837 leaves a remainder of 79. what will be th...
Short trick - 79/31 leaves a remainder of 17. That's the answer.
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A number when divided by 837 leaves a remainder of 79. what will be the remainder when the same number is divided by 31? answer is 17, please explain.?
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A number when divided by 837 leaves a remainder of 79. what will be the remainder when the same number is divided by 31? answer is 17, please explain.? for CLAT 2025 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about A number when divided by 837 leaves a remainder of 79. what will be the remainder when the same number is divided by 31? answer is 17, please explain.? covers all topics & solutions for CLAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number when divided by 837 leaves a remainder of 79. what will be the remainder when the same number is divided by 31? answer is 17, please explain.?.
A number when divided by 837 leaves a remainder of 79. what will be the remainder when the same number is divided by 31? answer is 17, please explain.? for CLAT 2025 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about A number when divided by 837 leaves a remainder of 79. what will be the remainder when the same number is divided by 31? answer is 17, please explain.? covers all topics & solutions for CLAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number when divided by 837 leaves a remainder of 79. what will be the remainder when the same number is divided by 31? answer is 17, please explain.?.
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