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The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The product of two numbers is 2028 and their H.C.F. is 13. The number ...
Let the numbers 13a and 13b.
Then, 13a x 13b = 2028
⇒ ab = 12.
Now, the co-primes with product 12 are (1, 12) and (3, 4).
[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]
So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4).
Clearly, there are 2 such pairs.
Then, 13a x 13b = 2028
⇒ ab = 12.
Now, the co-primes with product 12 are (1, 12) and (3, 4).
[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]
So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4).
Clearly, there are 2 such pairs.
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The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer?
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The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer? for UGC NET 2025 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UGC NET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer?.
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