Find the HCF of the following numbers using division method
312, 272 and 336

Answer

To find the HCF (Highest Common Factor) of the numbers 312, 272, and 336 using the division method, we can follow these steps:

### Step 1: Find HCF of the first two numbers (312 and 336)
1. **Set up the division:** We will divide the larger number (336) by the smaller number (312).
\[ 336 \div 312 \]
- 336 goes into 312 once (1) with a remainder.
- Calculate the remainder:
\[ 336 - 312 \times 1 = 336 - 312 = 24 \]

2. **Now, divide the previous divisor (312) by the remainder (24):**
\[ 312 \div 24 \]
- 24 goes into 312 twelve times (12).
- Calculate the remainder:
\[ 312 - 24 \times 12 = 312 - 288 = 24 \]

3. **Now, divide the previous divisor (24) by the remainder (0):**
\[ 24 \div 0 \]
- Since the remainder is now 0, the last non-zero remainder is the HCF of 312 and 336, which is 24.

### Step 2: Find HCF of the result (24) and the third number (272)
1. **Set up the division:** Now we will divide 272 by 24.
\[ 272 \div 24 \]
- 24 goes into 272 eleven times (11).
- Calculate the remainder:
\[ 272 - 24 \times 11 = 272 - 264 = 8 \]

2. **Now, divide the previous divisor (24) by the remainder (8):**
\[ 24 \div 8 \]
- 8 goes into 24 three times (3).
- Calculate the remainder:
\[ 24 - 8 \times 3 = 24 - 24 = 0 \]

3. **Since the remainder is now 0, the last non-zero remainder is the HCF of 272 and 24, which is 8.**

### Conclusion
The HCF of the numbers 312, 272, and 336 is **8**.

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