Question

the product of two number is 6760 and their hcf is 13 how many such pair can be formed​

Answer 1

product of no. = product of hcf and lcm.

6760= 13x

x = 6760÷13= 128.46

mens it is not possible

Answer 2

There can be 2 pairs of such numbers when product of two number is 6760 and their hcf is 13

Solution:

Let the two numbers be x and y

HCF = 13

Thus two numbers be 13x and 13y

product of two number is 6760

$13x \times 13y = 6760\\\\xy = \frac{6760}{169}\\\\xy = 40$

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

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 is: (13x , 13y)

(104, 65)

(13, 520)

Thus can be 2 pairs of such numbers

Learn more:

The product of two numbers is 12960 and their HCF is 36. How many pairs of such numbers can be formed?

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The sum of two numbers is 135 and their HCF is 9.

How many such pairs of numbers can be formed?​

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