# 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:
1
2
3
4
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:
85 comments Page 1 of 9.

Sheshank said:   1 year ago
@All.

Co prime means the numbers which we take, their HCF should be 1.

If we take (2, 6) their HCF is not one so we don't consider that.
(1)

(2, 6) are not co prime numbers.

As.
2=1*2.
6=1*6, 2*3;.

So for 6. (2) is again a factor so they can't be.

Nikhil G said:   3 years ago
@All.

1*12 = 1*3*2*2.
12*1 = 1*3*2*2.
2*6 = 3*2*2.
6*2 = 3*2*2.
3*4 = 3*2*2.
4*3 = 3*2*2.

So possible pairs are only 2.
(1)

(1*13, 12*13) (3*13, 4*13) (12*13, 1*13) (4*13, 3*13) these are four possible pairs.

Chaitanya said:   3 years ago
Take 13x*13y( because HCF is 13)
Let 13x*13y=2028
xy=2028/13*13
xy becomes 12.

Next find out the coprimes which should be the form of x,y hence,
coprimes are (1,12) and (3,4)or (4,3),
so the real pair will be;
(13*1,13*12)and (13*3,13*4),

Subham said:   3 years ago
The factors that is said to be co prime only when their GSF OR HCF is 1.

Umesh said:   3 years ago
The answer is incorrect. The answer could also be 2 and 6.

Randy Ranjith said:   4 years ago
Then why we take (4, 3) 4 is not co-prime?
(1)

Julie said:   4 years ago
Thank you for giving the clear answer @Snehesh.
(1)

Shahrukh said:   4 years ago
If 13x * 13y = 2028 then;

It should have been 13(x*y)= 2028
And x*y= 156
But your solution is telling that
13*13(x*y)= 2028.
x*y = 2028/ 169 = 12.
So , x*y = 12.

I mean why divided by 169 why not by 13 after taking common 13? Please tell me.
(2)