Question

the greatest no. which divides 134 and 167 leaving 2 as remainder in each case is-?

Answer 1

134-2=132
167-2=165
take HCF of 132 and 165
$132 = 2 \times 2 \times 3 \times 11 \\ 165 = 3 \times 5 \times 11$
HCF=3 X 11=33
The greatest number which divides both numbers,living 2 remainder in each case is 33.

Answer 2

The largest number which divides 615 and 963 leaving remainder 2 in each case => HCF.

And let the HCF be x.

To make 134 and 167 completely divisible by x we have to sub. 2 from 134 and 167.

134-2=132,167-2=165 

165 = 3*5*11

132= 2*2*3*11

⇒ x =3*11⇒x=33

Therefore the greatest number which divides 134 and 167 leaving 2 as remainder in each case as 33.