Question

The H.C.F of two numbers is 43 and their sum is 430. Total number of distinct pairs of two such numbers is

Answer 1

Given :

The  H.C.F of two numbers is 43

The sum of two number = 430

To Find :

Total number of distinct pairs of two such numbers

Solution :

∵ H.C.F of numbers = 43

Let the number = 43 x , 43 y

where x , y are co-prime

The sum of number = x + y

i.e   43 x + 43 y = 430          

Or,  x + y = $\dfrac{430}{43}$

∴     x + y = 10

Possible pairs = ( 1 , 9 ) ( 2 , 8 ) ( 3 , 7 ) ( 4 , 6 ) ( 5 , 5 )

Hence, Total number of distinct pairs of two such numbers are  ( 1 , 9 ) ( 2 , 8 ) ( 3 , 7 ) ( 4 , 6 ) ( 5 , 5 )  Answer