If H.C.F (225, 60)=225 × 5 – 10 x. Then find the value of x.

Given that the H.C.F. of 225 and 60 = (225 × 5) – 10x

The H.C.F of 225 and 60 by prime factorization method is

Prime factors of 225 = 5 × 5 × 3× 3 = 5² × 3²

Prime factors of 60 = 2 × 2 × 5 × 3 = 2² × 5 × 3

H.C.F is the product of lowest power of the common prime factors

⇒ H.C.F. = 3 × 5

= 15

Now, according to the given condition

H.C.F. of 225 and 60 = (225 × 5) – 10x

⇒ 15 = (225 × 5) – 10x

⇒ 15 = 1125 – 10x

⇒ 15 – 1125 = – 10x

⇒ – 1110 = – 10x

⇒ x = 111