Question

the sum of two numbers is 484 their h.c.f is 11. the number of such possible pairs is[

Answer 1

HCF = 11

So both numbers should have 11 as common factors. in factors of 484 (2 x 2 x 11 x 11) there are two 11 are there. So we can take 11 as one number

one number = 11

second number = 484 - 11 = 473

Answer 2

Answer:  There are 22 pairs

Step-by-step explanation:

As given:

H.C.F of the numbers is 11

Let the first number = 11x

second number = 11y

Now the sum of two numbers is 484

Therefore

$11x+ 11y = 484\\\\\text { dividing the whole equation by 11 we get }\\\\\Rightarrow x+y = 44$

the possible solution of x+y= 44 are

(x , y ) are (1,43) ,(2,42) , (3,41) , (4,40 ) ,  (5,39) , (6,38) , (7,37) , (8,36) , (9,35) , (10,34) , (11,33) , (12,32) , (13,31) , (14,30) , (15,29) , (16,28) , (17,27) , (18,26) , (19,25) , (20,24) , (21,23) , (22,22)

Hence, the possible such pairs are 22