Question

What is HCF of 72, 108 and 180 (Solve by long division method)?

Answer 1

HCF of 72, 108 and 180 can be represented as HCF of (HCF of 72, 108) and 180.

HCF(72, 108, 180) can be thus calculated by first finding HCF(72, 108) using long division and thereafter using this result with 180 to perform long division again.

Step 1: Divide 108 (larger number) by 72 (smaller number).

Step 2: Since the remainder $\ne$0, we will divide the divisor of step 1 (72) by the remainder (36). Repeat this process until the remainder = 0.

$\Rightarrow$ HCF(72, 108) = 36.

Step 3: Now to find the HCF of 36 and 180, we will perform a long division on 180 and 36.

Step 4: For remainder = 0, divisor = 36 $\Rightarrow$ HCF (36, 180) = 36

Thus, HCF (72, 108, 180) = HCF(HCF(72, 108), 180) = 36.