Find the highest common factor (H.C.F.) of 36 and 84.

Given data

• Numbers: 36 and 84.

Concept / Approach

• Use prime factorization or Euclidean algorithm to find H.C.F.

Step-by-step (prime factorization)

36 = 2^2 × 3^284 = 2^2 × 3 × 7Common prime powers: 2^2 × 3 = 4 × 3 = 12.

Alternative (Euclidean)

84 mod 36 = 12, 36 mod 12 = 0 ⇒ H.C.F. = 12.

Final Answer

H.C.F. = 12.