Aptitude - Problems on H.C.F and L.C.M - Discussion

How to choose the pairs?

I think the question have its answer.

The product of two numbers is 2028.

The Number of such pairs is 2.

Whatever it is, only 2 pairs, because we have only a and b, if we have a, b, c, d then we may have more pairs.

2 x 6
3 x 4
4 x 3
1 x 12
12 x 1
6 x 2

Correct me if I'm wrong.

Why they take the two pair like (1, 12), (3, 4)?

Why not (12, 1), (4, 3)?

I followed this method:

13a * 13b = 2028.
13ab = 2028.
ab = 156.

Now try to find the unique pairs (Prime factorize) forming 156:
2 * 78, 3 * 52.

So there are just 2 pairs. Hence, ans is 2.

Only 2 pairs is correct. Know the meaning of co-prime first "two numbers are said to be coprime if their H.C.F is 1 "which suits only the (1, 12) and (3, 4) pairs.

Guys, 2 and 6 are not co-primes, that means 2 is divided only by 1 and 6 is divided by both 2 and 3.

Co primes are the numbers where they should be divided only by one, in this case, they are 3 and 4.

Well, many of you got confused with Prime, co-Prime, why not (2,6) and all.....!!!

Lets we will Understood what's the question is ...!!!

The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:

step 1 : A * B = 2028 (Let A & B makes 2028 on multiply)
step 2 : (x*13) * (y*13) = 2028 (as mentioned HCF=13 for both A & B, so I took it as A=x*13, B=y*13)

******Note : HCF in the sense, only one number should be common in both A & B, hence it is 13 none other should be...!! ( are you cleared ??)*****

step 3 : x*y=2028/13*13
step 4 : x * y = 12 ( Product of X and Y makes 12, so we will separate 12 for and x & y)

*** The Sub-multiples of 12 are (1,12) (2,6) (3,4) .....still now ok...!! (Once again remember the NOTE..plzz)****

case 1 : (1,12)
A = 1 * 13
B = 12 * 13 (Product of A & B makes 2028, fine) also only 13 is common in both A & B. Hence it is satisfied

case 2 : (3,4)

A = 13 * 3
B = 13 * 4 ( Here also only 13 is common in both A & B. Hence this also satisfied )

case 3 : (2,6)

A = 13 * 2
B = 13 * 6(also 39 * 2 )

See clearly in both A and B the common numbers are 13 as well 2. It shouldn't be according to our NOTE

Hence this is not a correct pair with HCF as 13 alone. So it is said to not co-prime

JUST FOR UNDERSTANDING BIG DESCRIPTION..!! Paper Pen practice works faster ..!! ATB

I can't understand this. Please help me to get it.

Another way I'm telling you without co-primes.

2028/13=156, again divide 156/13 = 12.
Now factorize 12 = 1, 12, 3, 4.
There are 4 numbers so the pair is 2.

Why we can't use the pair (4, 3) & (12, 1). We are asked to find the total number of such pairs. So (1, 12), (3, 4), (4, 3), (12, 1)?