There are 156 students in an after school program. The program director would like to split the students into groups of equal sizes with no students left over. She wants at least 4 but no more than 12 students in each group. Describe the possible number of groups and students in each group?

To determine the possible number of groups and the number of students in each group, we need to find the divisors of 156 that are between 4 and 12.

### Step 1: Find all divisors of 156
We start by determining the divisors of 156:
- 156 ÷ 1 = 156
- 156 ÷ 2 = 78
- 156 ÷ 3 = 52
- 156 ÷ 4 = 39
- 156 ÷ 6 = 26
- 156 ÷ 12 = 13

The divisors of 156 are: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, and 156.

### Step 2: Identify divisors between 4 and 12
From the list above, the divisors between 4 and 12 are:
- 4
- 6
- 12

### Step 3: Calculate the number of groups for each divisor
For each of these divisors, we can calculate the number of groups:
- If there are 4 students per group: 156 ÷ 4 = 39 groups
- If there are 6 students per group: 156 ÷ 6 = 26 groups
- If there are 12 students per group: 156 ÷ 12 = 13 groups

### Final Answer:
The possible group sizes and corresponding number of groups are:
- 39 groups with 4 students each
- 26 groups with 6 students each
- 13 groups with 12 students each

Would you like more details or have any questions about this?

---

Here are 5 related questions to explore:
1. How do you find the divisors of a number systematically?
2. What is the prime factorization of 156?
3. How would the answer change if the maximum group size was 15 instead of 12?
4. How can we use the greatest common divisor (GCD) to solve similar problems?
5. What if the program director wanted to maximize the number of groups?

**Tip:** When looking for divisors of a number, try dividing by smaller integers first to avoid missing any!

Explore how to divide 156 students into groups of equal sizes with no students left over. Learn about divisibility rules and discover the possible group sizes and corresponding number of groups, such as 39 groups with 4 students each, 26 groups with 6 students each, and 13 groups with 12 students each. Ideal for students in Grades 5-7.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation