# 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 13*a* and 13*b*.

Then, 13*a* x 13*b* = 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:

91 comments Page 9 of 10.
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) ?

Priyanka said:
1 decade ago

Yes why not 2, 6 even when they will also give 2028 on (13*2, 13*6) ?.

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