Three piece of timber 24 m , 28.8 m and 33.6 m long have to be divided into planks of the same length. What is the greatest possible length of each plank ?

Options

A. `8.4` m
B. `4.8` m
C. `4.5` m
D. `5.4` m

Answer

To find the greatest possible length of each plank that can be cut from the three pieces of timber measuring 24 m, 28.8 m, and 33.6 m, we need to determine the highest common factor (HCF) of these three lengths. Here’s how to do it step by step:

### Step 1: Convert all lengths to the same unit
Since 28.8 m and 33.6 m are in decimal form, we can convert them into fractions for easier calculation:
- 28.8 m = 288/10 = 144/5 m
- 33.6 m = 336/10 = 168/5 m

Now we have:
- 24 m
- 144/5 m
- 168/5 m

### Step 2: Find the HCF using the division method
We will find the HCF of the three numbers by using the division method.

1. **Find HCF of 24 and 28.8 (144/5)**:
- Divide 28.8 by 24:
\[ 28.8 \div 24 = 1 \quad \text{(1 time)} \]
- Subtract:
\[ 28.8 - 24 = 4.8 \]
- Now, divide 24 by the remainder (4.8):
\[ 24 \div 4.8 = 5 \quad \text{(5 times)} \]
- Since the remainder is 0, we have found that HCF(24, 28.8) = 4.8 m.

2. **Now find HCF of the result (4.8) and 33.6 (168/5)**:
- Divide 33.6 by 4.8:
\[ 33.6 \div 4.8 = 7 \quad \text{(7 times)} \]
- Since the remainder is 0, we have found that HCF(4.8, 33.6) = 4.8 m.

### Step 3: Conclusion
The greatest possible length of each plank that can be cut from the three pieces of timber is **4.8 meters**.