Aptitude - Problems on H.C.F and L.C.M - Discussion
Discussion Forum : Problems on H.C.F and L.C.M - General Questions (Q.No. 9)
9.
The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:
Answer: Option
Explanation:
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.
Discussion:
94 comments Page 5 of 10.
Shivangi said:
8 years ago
But Question is how many no of the pair. Not co factors. Please clear my doubt is no of pair means co-factor?
Santhosh said:
1 decade ago
1 is neither prime nor composite. In the solution it was given a co prime pair. So can it be co-prime pair ?
Veerabhadra said:
5 years ago
Why not answer is 4?
(1*13, 12*13) (3*13, 4*13) (12*13, 1*13) (4*13, 3*13) these are four possible pairs.
(1*13, 12*13) (3*13, 4*13) (12*13, 1*13) (4*13, 3*13) these are four possible pairs.
(1)
Gayathri said:
5 months ago
Why can't we take pairs as four because (12, 1) and (4, 3) count as well right?
Anyone please explain.
Anyone please explain.
Parmanand Singh said:
1 year ago
It should be 3 pairs because the co-prime of product 12 is (1, 12) (2, 6) (3, 4).
So we get, 3 pairs.
So we get, 3 pairs.
(24)
Abhishek s g said:
7 years ago
We should not take 2 and 6 because if we take 2 and 6, the product will be 2028 but HCF is 26 not 13.
Akshara said:
2 years ago
@Umesh.
No, it cannot be 2 and 6 because they are not coprime. 2 and 6 have 2 as a common factor.
No, it cannot be 2 and 6 because they are not coprime. 2 and 6 have 2 as a common factor.
(18)
Raji said:
1 decade ago
x * y = 2028
x * 13 = 2028
x = 156
156 = 13 * 12
and here 13 appears twice and so is the ans!!!
x * 13 = 2028
x = 156
156 = 13 * 12
and here 13 appears twice and so is the ans!!!
Aajush said:
1 decade ago
Its not compulsory to get from prime or co-prime.
The thing is to get it not exceeding 2 pair.
The thing is to get it not exceeding 2 pair.
Aish said:
1 decade ago
Why we can not take pair as (1, 12), (4, 3), (3, 4), (12, 1)?
I think it should be 4 pairs.
I think it should be 4 pairs.
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