Question

Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

Answer 1

In this case, we have to find HCF with the remainder

Step

1. Find the Differences between numbers
2. Get the HCF ( that differences)

We have here 43, 91 and 183

So differences are

183 - 91 = 92,

183 - 43 = 140,

91 - 43 = 48.

Now

HCF (48, 92 and 140)

As

$48=2\times 2\times 2\times 2\times 3,$

$92=2\times 2\times 23,$

$140=2\times 2\times 5\times 7$

$HCF=2\times 2=4.$

And 4 is the required number.