Question

Find the largest number which divides 615 and 963, leaving remainder 6 in each case.

Answer 1

Hint: Subtracting the remainder from the given numbers and finding the highest common factor gives the greatest number. That gives us the largest number.

Complete step-by-step answer:
The given numbers are 615 and 963
 Leaving 6 as remainder.
 Let us consider the number 615 first,
Here it was given that 615 when divided by the greatest number leaves the remainder as 6.
Similarly the number 963 when divided by the greatest number leaves the remainder as 6.
Now Considering 615 again.
The greatest number divides 615 and leaves the remainder as 6, that means we have to subtract 6 from 615.
$$615-6=609$$
Now writing the factors for 609 we get,
$$609=3\times 7\times 29$$

The greatest number divides 963 and leaves the remainder as 6, that means we have to subtract 6 from 963.
$$963-6=957$$.
Now writing the factors for 957 we get,
$$957=3\times 11\times 29$$
To find the greatest number that divides the 2 numbers, we have to find H.C.F (Highest common factor).
$$609=3\times 7\times 29$$
$$957=3\times 11\times 29$$
H.C.F of 609 and 957 is $$3\times 29$$= $$87$$.
Therefore the greatest number that divides 615 and 963 by leaving remainder 6 is 87.

Note: This is a direct problem with finding the greatest number by writing the factors. The basic step here is to subtract the remainder and then find the greatest number. Highest common factor gives the greatest number that divides the given number.