The HCF of 2 No = 12 & their product = 1728; find how many pairs possible?

Question

The HCF of 2 No = 12 & their product = 1728; find how many pairs possible?​

Madeline · Answer

Answer:   2 pairs are possible i.e   x=144 , y =12  or  x= -144 , y = -12

Kinsley · Answer

IsWhen product of numbers A and B, and the HCF are given, we find the LCM by using the identity H x L = A x B.

So, L = 1728 /12 = 144

LCM is always divisible by HCF.

L/H = 144/12 = 12

Now 12 can be split only as 1x 12 or 2×6 or 3 x 4

We take each pair and multiply the numbers in each pair by the HCF.

We get now the pairs (12, 144), (24, 72) and (36, 48)

The HCF of 2 No = 12& their product = 1728; find how many pairs possible?​