Firstly, the required numbers which on dividing doesn’t leave any remainder are to be found.
This is done by subtracting 6 from both the given numbers.
So, the numbers are 615 – 6 = 609 and 963 – 6 = 957.
Now, if the HCF of 609 and 957 is found, that will be the required number.
By applying Euclid’s division lemma
957 = 609 x 1+ 348
609 = 348 x 1 + 261
348 = 216 x 1 + 87
261 = 87 x 3 + 0.
⇒ H.C.F. = 87.
Therefore, the required number is 87.
