Find the greatest possible length which can be used to measure exactly the lengths `7 m`, `3 m` `85 cm` and `12 m` `95 cm`.

Explanation

To find the greatest possible length that can measure exactly the lengths of 7 m, 3 m 85 cm, and 12 m 95 cm, we will follow these steps:

### Step 1: Convert all lengths to the same unit
First, we need to convert all measurements to centimeters for consistency.

1. **Convert 7 m to cm**:
\[ 7 \text{ m} = 7 \times 100 \text{ cm} = 700 \text{ cm} \]

2. **Convert 3 m 85 cm to cm**:
\[ 3 \text{ m} 85 \text{ cm} = 3 \times 100 \text{ cm} + 85 \text{ cm} = 300 \text{ cm} + 85 \text{ cm} = 385 \text{ cm} \]

3. **Convert 12 m 95 cm to cm**:
\[ 12 \text{ m} 95 \text{ cm} = 12 \times 100 \text{ cm} + 95 \text{ cm} = 1200 \text{ cm} + 95 \text{ cm} = 1295 \text{ cm} \]

### Step 2: Find the HCF of the lengths
Now we need to find the highest common factor (HCF) of the three lengths: 700 cm, 385 cm, and 1295 cm.

1. **Prime factorization of 700**:
\[ 700 = 2^2 \times 5^2 \times 7 \]

2. **Prime factorization of 385**:
\[ 385 = 5 \times 7 \times 11 \]

3. **Prime factorization of 1295**:
\[ 1295 = 5 \times 7 \times 37 \]

### Step 3: Identify common factors
Now we identify the common prime factors from the factorizations:

- From 700: \(2^2, 5^2, 7\)
- From 385: \(5, 7, 11\)
- From 1295: \(5, 7, 37\)

The common prime factors are \(5\) and \(7\).

### Step 4: Calculate the HCF
The HCF is the product of the lowest powers of the common prime factors:

\[ \text{HCF} = 5^1 \times 7^1 = 5 \times 7 = 35 \]

### Conclusion
The greatest possible length that can measure exactly the lengths of 7 m, 3 m 85 cm, and 12 m 95 cm is **35 cm**.

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