H.C.F. of 54 and 336 is :

Options

A. 9
B. 3
C. 6
D. 18

Answer

To find the H.C.F. (Highest Common Factor) of 54 and 336, we can use the Euclidean algorithm. Here’s a step-by-step solution:

### Step 1: Divide the larger number by the smaller number
We start by dividing 336 by 54.

\[ 336 \div 54 = 6 \quad \text{(quotient)} \]
\[ 336 - (54 \times 6) = 336 - 324 = 12 \quad \text{(remainder)} \]

### Step 2: Replace the larger number with the smaller number and the smaller number with the remainder
Now, we take 54 and 12 and repeat the process.

\[ 54 \div 12 = 4 \quad \text{(quotient)} \]
\[ 54 - (12 \times 4) = 54 - 48 = 6 \quad \text{(remainder)} \]

### Step 3: Repeat the process with the new pair
Next, we take 12 and 6.

\[ 12 \div 6 = 2 \quad \text{(quotient)} \]
\[ 12 - (6 \times 2) = 12 - 12 = 0 \quad \text{(remainder)} \]

### Step 4: Conclusion
Since the remainder is now 0, the last non-zero remainder is the H.C.F. Therefore, the H.C.F. of 54 and 336 is:

\[ \text{H.C.F.} = 6 \]

### Final Answer:
The H.C.F. of 54 and 336 is 6.

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