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Find the remainder when 73 *75 *78 *57 *197 *37 is divided by 34.
- a)32
- b)30
- c)15
- d)28
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Find the remainder when 73 *75 *78 *57 *197 *37 is divided by 34.a)32b...
Remainder,
(73 *75 *78 *57 *197 *37)/34 ===> (5 *7 *10 *23 *27 *3)/34
[We have taken individual remainder, which means if 73 is divided by 34 individually, it will give remainder 5, 75 divided 34 gives remainder 7 and so on.]
(5 *7 *10 *23 *27 *3)/34 ===> (35 *30 *23 *27)/34 [Number Multiplied]
(35 *30 *23 *27)/34 ===> (1*-4*-11* -7)/34
[We have taken here negative as well as positive remainder at the same time. When 30 divided by 34 it will give either positive remainder 30 or negative remainder -4. We can use any one of negative or positive remainder at any time.]
(1 *-4 *-11 * -7)/34 ===> (28 *-11)/34 ===> (-6 *-11)/34 ===> 66/34 ===R===> 32.
Required remainder = 32.
Most Upvoted Answer
Find the remainder when 73 *75 *78 *57 *197 *37 is divided by 34.a)32b...
Solution:
To find the remainder when a large number is divided by a smaller number, we can use the concept of modular arithmetic.
Modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value called the modulus. In this case, the modulus is 34.
To find the remainder when 73 * 75 * 78 * 57 * 197 * 37 is divided by 34, we can use the following steps:
Step 1: Break down each factor into its remainder when divided by 34.
- 73 = 5 (because 73 divided by 34 leaves a remainder of 5)
- 75 = 7
- 78 = 10
- 57 = 23
- 197 = 21
- 37 = 3
Step 2: Multiply the remainders together.
5 * 7 * 10 * 23 * 21 * 3 = 1,952,100
Step 3: Find the remainder of the product when divided by 34.
1,952,100 divided by 34 leaves a remainder of 32.
Therefore, the remainder when 73 * 75 * 78 * 57 * 197 * 37 is divided by 34 is 32. The correct answer is option A.
To find the remainder when a large number is divided by a smaller number, we can use the concept of modular arithmetic.
Modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value called the modulus. In this case, the modulus is 34.
To find the remainder when 73 * 75 * 78 * 57 * 197 * 37 is divided by 34, we can use the following steps:
Step 1: Break down each factor into its remainder when divided by 34.
- 73 = 5 (because 73 divided by 34 leaves a remainder of 5)
- 75 = 7
- 78 = 10
- 57 = 23
- 197 = 21
- 37 = 3
Step 2: Multiply the remainders together.
5 * 7 * 10 * 23 * 21 * 3 = 1,952,100
Step 3: Find the remainder of the product when divided by 34.
1,952,100 divided by 34 leaves a remainder of 32.
Therefore, the remainder when 73 * 75 * 78 * 57 * 197 * 37 is divided by 34 is 32. The correct answer is option A.
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Find the remainder when 73 *75 *78 *57 *197 *37 is divided by 34.a)32b)30c)15d)28Correct answer is option 'A'. Can you explain this answer?
Question Description
Find the remainder when 73 *75 *78 *57 *197 *37 is divided by 34.a)32b)30c)15d)28Correct answer is option 'A'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Find the remainder when 73 *75 *78 *57 *197 *37 is divided by 34.a)32b)30c)15d)28Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the remainder when 73 *75 *78 *57 *197 *37 is divided by 34.a)32b)30c)15d)28Correct answer is option 'A'. Can you explain this answer?.
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