Find the HCF of : 1632, 2976 and 3552

Options

A. `96`
B. `92`
C. `90`
D. `98`

Answer

To find the Highest Common Factor (HCF) of the numbers 1632, 2976, and 3552, we will use the method of division. We will take two numbers at a time and find their HCF, and then we will use that result to find the HCF with the third number.

### Step-by-Step Solution:

**Step 1: Find HCF of 1632 and 2976**

1. Divide the larger number (2976) by the smaller number (1632).
- 2976 ÷ 1632 = 1 (remainder 1344)
- Remainder = 2976 - 1632 = 1344

2. Now, take the previous divisor (1632) and divide it by the remainder (1344).
- 1632 ÷ 1344 = 1 (remainder 288)
- Remainder = 1632 - 1344 = 288

3. Next, take the previous divisor (1344) and divide it by the remainder (288).
- 1344 ÷ 288 = 4 (remainder 192)
- Remainder = 1344 - (288 * 4) = 1344 - 1152 = 192

4. Now, take the previous divisor (288) and divide it by the remainder (192).
- 288 ÷ 192 = 1 (remainder 96)
- Remainder = 288 - 192 = 96

5. Finally, take the previous divisor (192) and divide it by the remainder (96).
- 192 ÷ 96 = 2 (remainder 0)
- Remainder = 192 - (96 * 2) = 0

Since the remainder is now 0, the HCF of 1632 and 2976 is 96.

**Step 2: Find HCF of 96 and 3552**

1. Now, we will find the HCF of 96 and 3552.
- 3552 ÷ 96 = 37 (remainder 0)
- Remainder = 3552 - (96 * 37) = 0

Since the remainder is 0, the HCF of 96 and 3552 is also 96.

### Conclusion:
The HCF of 1632, 2976, and 3552 is **96**.

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