Question

the product of two numbers is 3468, then what could be the maximum value of their HCF

Answer 1

Step-by-step explanation:

Let us consider that the two numbers are,

13x and 13y.

As (13x,13y) and (13y,13x) represent the same pair we will consider only one of them.

Given that the product of two numbers is 6760.

So, 13x*13y=6760

or, 169xy=6760

or, xy=40

So the pair (x,y)=(8,5),(4,10),(2,20),(1,40)

But for the HCF to be 13, the pair (x,y) must not have any common factor (other than 1)

So the pair (x,y)=(8,5),(1,40)

So, the pair of numbers will be:

{13x,13y}

(104,65)

(13,520)

But, if the order of number is important then there will be another two pair of numbers:

(65,104)

(520,13)

Thanks for reading my answer. Hope this helps