Question

Let d is hcf of 24,36 find a+ b if d equal to 24a+ 36b

Answer 1

solution
d =hcf of 24 and 36
to find : a and b such that d = 24a + 36b

applying Euclid 's division lemma to 24 and 36 we get
36 =24*1 +12...(1)
24=2*12+0thus hcf of 24 and 36 is 12.
from (1) we have ,
12=36-24
12=24(-1)+36(1)
12=24a-36b
where a =-1 and b = 1, is answer

Answer 2

HCF of any numbers means product of their common divisors

  24 = 2*2*2*3

  36 = 2*2*3*3 
  
  common factors are 2*2*3 = 12

   HCF is 12

   Now, 24a +36b =12

           12(2a + 3b) = 12

             2a +3b = 1  

        Therefore , a = -1 & b =1