Find the largest positive integer that will divide 122, 150 and 115 leaving remainders 5, 7 and 11 respectively?

The largest positive integer that will be

122 – 5 = 117 ⇒ 117 = 3 × 3 × 13

150 – 7 = 143 ⇒ 143 = 11× 13

115 – 11 = 104 ⇒ 104 = 2 × 2 × 2 × 13

The H.C.F. of 117, 143 and 104 is 13

So, the largest number which divides 122, 150 and 115 leaving 5, 7 and 11 remainder respectively is 13