The H.C.F. of 64 and 96 will be :

Options

A. `12`
B. `16`
C. `18`
D. `32`

Answer

To find the H.C.F. (Highest Common Factor) of 64 and 96, we can use the method of division (Euclidean algorithm). Here’s the step-by-step solution:

### Step 1: Divide the larger number by the smaller number.
- We start with the two numbers: 96 and 64.
- Divide 96 by 64.

\[ 96 \div 64 = 1 \quad \text{(quotient)} \]
\[ \text{Remainder} = 96 - (64 \times 1) = 96 - 64 = 32 \]

### Step 2: Replace the larger number with the smaller number and the smaller number with the remainder.
- Now we take the smaller number (64) and the remainder (32).
- Divide 64 by 32.

\[ 64 \div 32 = 2 \quad \text{(quotient)} \]
\[ \text{Remainder} = 64 - (32 \times 2) = 64 - 64 = 0 \]

### Step 3: When the remainder is 0, the divisor at this step is the H.C.F.
- Since the remainder is now 0, we take the last divisor, which is 32.

Thus, the H.C.F. of 64 and 96 is **32**.

### Final Answer:
H.C.F. of 64 and 96 is **32**.

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