Question

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

Answer 1

Step-by-step explanation:

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

615−6=609

Now writing the factors for 609 we get,

609=3×7×29

609=3×7×29

The greatest number divides 963 and leaves the remainder as 6, that means we have to subtract 6 from 963.

963−6=957

963−6=957

.

Now writing the factors for 957 we get,

957=3×11×29

957=3×11×29

To find the greatest number that divides the 2 numbers, we have to find H.C.F (Highest common factor).

609=3×7×29

609=3×7×29

957=3×11×29

957=3×11×29

H.C.F of 609 and 957 is 3×29

3×29

= 87

87

.

Therefore the greatest number that divides 615 and 963 by leaving remainder 6 is 87.

Answer 2

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

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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=3×7×29

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=3×11×29

To find the greatest number that divides the 2 numbers, we have to find H.C.F (Highest common factor).

609=3×7×29

957=3×11×29

H.C.F of 609 and 957 is 3×29

= 87

.

Therefore the greatest number that divides 615 and 963 by leaving remainder 6 is 87.