Following is a problem from text book of Class V.
"There are 4 poles of measure 105 cm, 215 cm, 150 cm and 235 cm respectively. If they have to be cut into pieces of equal length, what is the maximum length of each piece?" This question is asked to

Options

A. give practice of word problems based on HCF and LCM
B. test knowledge of factors and multiples
C. check the skill of finding HCF
D. enhance problem solving skills using learnt concepts

Answer

To solve the problem of finding the maximum length of each piece that the poles can be cut into, we need to determine the highest common factor (HCF) of the lengths of the poles. The lengths of the poles are 105 cm, 215 cm, 150 cm, and 235 cm.

### Step-by-Step Solution:

**Step 1: List the lengths of the poles.**
- The lengths are: 105 cm, 215 cm, 150 cm, and 235 cm.

**Step 2: Find the prime factorization of each length.**
- **105**:
- 105 = 3 × 5 × 7
- **215**:
- 215 = 5 × 43
- **150**:
- 150 = 2 × 3 × 5²
- **235**:
- 235 = 5 × 47

**Step 3: Identify the common factors.**
- The only common factor among all the prime factorizations is **5**.

**Step 4: Determine the maximum length of each piece.**
- Since the highest common factor is 5, the maximum length of each piece that the poles can be cut into is **5 cm**.

### Final Answer:
The maximum length of each piece is **5 cm**.