What is the greatest number that will divide 99, 147 and 219 leaving the same reminder in each case?

• A. 22
• B. 23
• C. 24
• D. 25

Answer: (C)

Given that, a = 99, b = 147,  c = 219     Required number = [H.C.F. of (a-b), (b-c), (c-a)]               Now,                             (a-b)  = (99 – 147) = 48                            (b-c)  = (147 – 219) = 72                            (c-a) =   (219 – 99) = 120             Also                          48 = 24 x 3¹           72 = 23 x 32           120 = 23 x 3¹ x 5¹           ∴ HCF of 48,72 and 120 = 23 x 3¹ = 8 x 3  = 24