text: # Find the largest number which divides 615 and 963 leaving remainder 6 in each case.
  
  Question:
  
  Find the largest number which divides 615 and 963 leaving remainder 6 in each case.
  
  Solution:
  
  We need to find the largest number which divides 615 and 963 leaving remainder 6 in each case.
  
  The required number when divides 615 and 963 , leaves remainder 6 , this means $615-6=609$ and $963-6=957$ are completely divisible by the number.
  
  Therefore,
  
  The required number = H.C.F. of 609 and 957.
  
  By applying Euclid’s division lemma
  
  $957=609 \times 1+348$
  
  $609=348 \times 1+261$
  
  $348=216 \times 1+87$
  
  $261=87 \times 3+0$
  
  Therefore, H.C.F. = 87.
  
  Hence, the required number is 87 .