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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?
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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 × 13b = 2028
ab = 12.
Now, the co-primes with product 12 are (1, 12) and (3, 4).
So, the required numbers are (13 × 1, 13 × 12) and (13 × 3, 13 × 4).
Clearly, there are 2 such pairs.
ab = 12.
Now, the co-primes with product 12 are (1, 12) and (3, 4).
So, the required numbers are (13 × 1, 13 × 12) and (13 × 3, 13 × 4).
Clearly, there are 2 such pairs.
Most Upvoted Answer
The product of two numbers is 2028 and their H.C.F. is 13. The number ...
Given Information:
The product of two numbers is 2028 and their H.C.F. is 13.
Solution:
Finding the Prime Factorization of 2028:
- The prime factorization of 2028 is 2 x 2 x 3 x 13 x 13.
Finding the pairs of numbers:
- Since the H.C.F. is 13, the two numbers must have 13 as a factor.
- Therefore, the two numbers can be written as 13a and 13b, where a and b are coprime.
- The product of the two numbers is 2028, so (13a)(13b) = 2028.
- Simplifying, we get ab = 12.
Finding the pairs:
- The pairs of numbers that satisfy ab = 12 are:
- (1, 12) and (12, 1)
- (2, 6) and (6, 2)
- (3, 4) and (4, 3)
Number of such pairs:
- There are 2 pairs of numbers that satisfy the given conditions.
- Therefore, the number of such pairs is 2.
Therefore, the correct answer is option B) 2.
The product of two numbers is 2028 and their H.C.F. is 13.
Solution:
Finding the Prime Factorization of 2028:
- The prime factorization of 2028 is 2 x 2 x 3 x 13 x 13.
Finding the pairs of numbers:
- Since the H.C.F. is 13, the two numbers must have 13 as a factor.
- Therefore, the two numbers can be written as 13a and 13b, where a and b are coprime.
- The product of the two numbers is 2028, so (13a)(13b) = 2028.
- Simplifying, we get ab = 12.
Finding the pairs:
- The pairs of numbers that satisfy ab = 12 are:
- (1, 12) and (12, 1)
- (2, 6) and (6, 2)
- (3, 4) and (4, 3)
Number of such pairs:
- There are 2 pairs of numbers that satisfy the given conditions.
- Therefore, the number of such pairs is 2.
Therefore, the correct answer is option B) 2.
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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 Class 5 2024 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 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 Class 5 2024 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?.
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 Class 5 2024 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 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 Class 5 2024 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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