Question

The H.C.F of 3556 and 3444 is:

• A. 14
• B. 84
• C. 56
• D. 28

Hint:

Use the Euclidean algorithm to find the HCF by repeatedly applying division and finding the remainder until it is 0.

Answer 1

The Correct Option is D

To find the H.C.F of 3556 and 3444, we can use the Euclidean algorithm. \[ 3556 \div 3444 = 1 \quad \text{(quotient)} \quad 3556 - 3444 = 112 \quad \text{(remainder)}. \] Next, apply the algorithm to 3444 and 112: \[ 3444 \div 112 = 30 \quad \text{(quotient)} \quad 3444 - (30 \times 112) = 3444 - 3360 = 84 \quad \text{(remainder)}. \] Now, apply the algorithm to 112 and 84: \[ 112 \div 84 = 1 \quad \text{(quotient)} \quad 112 - 84 = 28 \quad \text{(remainder)}. \] Finally, apply the algorithm to 84 and 28: \[ 84 \div 28 = 3 \quad \text{(quotient)} \quad 84 - (3 \times 28) = 84 - 84 = 0 \quad \text{(remainder)}. \] Since the remainder is 0, the H.C.F is 28.