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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?
Most Upvoted Answer
The product of two numbers is 2028 and their H.C.F. is 13. The number...
Explanation
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).
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 × 1, 13 × 12) and (13 × 3, 13 × 4).
Clearly, there are 2 such pairs.
Hence, the correct option is (B).
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The product of two numbers is 2028 and their H.C.F. is 13. The number...
Given:
The product of two numbers is 2028 and their H.C.F. is 13.
Solution:
Finding the prime factorization of 2028:
2028 = 2 x 2 x 3 x 13 x 13
Expressing 2028 as a product of two numbers:
Since the H.C.F. of the two numbers is 13, we can express 2028 as 13 x (156), where 156 is the other factor.
Finding the prime factorization of 156:
156 = 2 x 2 x 3 x 13
Expressing 156 as a product of two numbers:
156 = 1 x 156 or 2 x 78 or 3 x 52 or 4 x 39 or 6 x 26 or 12 x 13
Combining the factors:
We have pairs of factors (13, 156) and (26, 78) which satisfy the conditions.
Therefore, the number of such pairs is 2, which corresponds to option B.
The product of two numbers is 2028 and their H.C.F. is 13.
Solution:
Finding the prime factorization of 2028:
2028 = 2 x 2 x 3 x 13 x 13
Expressing 2028 as a product of two numbers:
Since the H.C.F. of the two numbers is 13, we can express 2028 as 13 x (156), where 156 is the other factor.
Finding the prime factorization of 156:
156 = 2 x 2 x 3 x 13
Expressing 156 as a product of two numbers:
156 = 1 x 156 or 2 x 78 or 3 x 52 or 4 x 39 or 6 x 26 or 12 x 13
Combining the factors:
We have pairs of factors (13, 156) and (26, 78) which satisfy the conditions.
Therefore, the number of such pairs is 2, which corresponds to option B.
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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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