In a school the number of students in Grades 4,5 and 6 were 215, 258 and 301 respectively. If every grade was divided in sections and every section had the same number of students, what was the minimum number of sections in all in these three classes?

Options

A. 15
B. 17
C. 18
D. 16

Answer

To solve the problem, we need to find the minimum number of sections for Grades 4, 5, and 6, given the number of students in each grade. The number of students in each grade is as follows:

- Grade 4: 215 students
- Grade 5: 258 students
- Grade 6: 301 students

We will follow these steps:

### Step 1: Find the Highest Common Factor (HCF) or Greatest Common Divisor (GCD) of the three numbers.

To do this, we will factor each number:

1. **Factor 215:**
- 215 = 5 × 43

2. **Factor 258:**
- 258 = 2 × 3 × 43

3. **Factor 301:**
- 301 = 7 × 43

Now, we identify the common factor from the factorizations. The common factor is 43.

### Step 2: Calculate the number of sections for each grade.

Now that we have the HCF (43), we can find out how many sections there will be in each grade by dividing the total number of students in each grade by the number of students per section (which is 43).

1. **For Grade 4:**
- Number of sections = Total students in Grade 4 / HCF
- Number of sections = 215 / 43 = 5 sections

2. **For Grade 5:**
- Number of sections = Total students in Grade 5 / HCF
- Number of sections = 258 / 43 = 6 sections

3. **For Grade 6:**
- Number of sections = Total students in Grade 6 / HCF
- Number of sections = 301 / 43 = 7 sections

### Step 3: Calculate the total number of sections.

Now, we add the number of sections from all grades to find the minimum total number of sections:

- Total sections = Sections in Grade 4 + Sections in Grade 5 + Sections in Grade 6
- Total sections = 5 + 6 + 7 = 18 sections

### Conclusion:

The minimum number of sections in all three classes is **18**.

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