Find the G.C.D. (H.C.F.) of 1.08, 0.36 and 0.90.

Given data

• Decimals: 1.08, 0.36, 0.90

Concept / Approach

• To compute G.C.D. of decimals, clear decimals by multiplying all numbers by 10^k, where k is the maximum number of decimal places.
• After finding the G.C.D. of the integers, divide back by the same 10^k.

Step-by-step calculation

Max decimal places = 2 ⇒ multiply by 100.Numbers become: 108, 36, 90.GCD(108, 36) = 36.GCD(36, 90) = 18.Hence integer G.C.D. = 18 ⇒ decimal G.C.D. = 18 ÷ 100 = 0.18.

Verification

Check: 1.08 ÷ 0.18 = 6; 0.36 ÷ 0.18 = 2; 0.90 ÷ 0.18 = 5 ⇒ all integers.

Common pitfalls

• Using average or minimum instead of G.C.D.
• Forgetting to scale back after finding the integer G.C.D.

Final Answer

G.C.D. = 0.18.