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:
92 comments Page 9 of 10.
Utsavchavda said:
1 decade ago
Meaning of co-prime ?
Vaani said:
1 decade ago
Why should we take co-primes?
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!!!
Puja said:
1 decade ago
A co-prime no. is that in which no common factor other than 1.
Like in the above proble factor will be (3,4) bcoz common factor b/w them is only 1.
But if we take factor like (2,6) then common factor b/w them will be 1 and 2. So as these are not common factor hence we will not consider this.
@Sujay: you cn take (4,3) instead of (3,4)... ans will be same.
Like in the above proble factor will be (3,4) bcoz common factor b/w them is only 1.
But if we take factor like (2,6) then common factor b/w them will be 1 and 2. So as these are not common factor hence we will not consider this.
@Sujay: you cn take (4,3) instead of (3,4)... ans will be same.
Sujay said:
1 decade ago
No of pairs are (1, 12) , (3, 4). This is given in solution. But another pair we can consider here (4, 3) ? please explain this ?.
Nikhil said:
1 decade ago
In that case HCF would become 26.
Giri said:
1 decade ago
2 and 6 r not co-primes bcoz 6 has 2 as factor
whereas for 3 and 4 have no common factors except 1
whereas for 3 and 4 have no common factors except 1
Jaz said:
1 decade ago
Explain this.
Raj said:
1 decade ago
2,6 r not co-primes.see the notes given above.
Sai said:
1 decade ago
Why (2, 6) ?
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