Question

The sum of two numbers is 1056 and their hcf is 66 find the number of such pair

Answer 1

Answer:

Number of such pairs=4

Given:

Sum of two numbers=1056 and their H.C.F=66

To find:

Number of such pairs

Solution:-

Let the numbers be 66x and 66y

Then

According to question

$66x + 66y = 1056$

$66(x + y) = 1056$

$x + y = \frac{1056}{66}$

$x + y = 16$

If x+y=16

Then numbers can be

•x=15;y=1

•x=11;y=5

•x=9;y=7

•x=3;y=13

Checking all the numbers

{66 ×15+66×1}=1056

{66 ×11+66×5}=1056

{66 ×3+66×13}=1056

{66 ×9+66×7}=1056

------------------------

Therefore;

Number of such pairs is 4