There are 24 students in Mrs. Garcia's class. She wants to divide the class evenly into groups of at least 4 students. Write the ways in which she can divide the class?
I got 6 ways but I need to explain more. This is under my prime factorization unit.
there are no other ways maybe there are but i don't know
but can u give us the answer pls i want to go play and this is my last question dudes plss
The question asks us to make groups with AT LEAST 4 students in each. So, 3 groups with 8 in each also works. And 2 groups with 12 in each works. Pay attention to detail.
To find the different ways Mrs. Garcia can divide her class of 24 students into groups of at least 4 students, we can use prime factorization.
The prime factorization of 24 is 2^3 * 3^1, where 2 and 3 are prime numbers.
When dividing the class into groups, we want to ensure that each group has at least 4 students. This means we need to find the combinations of the prime factors that are greater than or equal to 4.
Let's start by looking at the possibilities for the number of 2s in each group. Since 2^2 = 4, we can have either 2 or 3 groups with 2 students each (2^2 * 3^1 / 2^2 = 3^1 = 3 groups of 2).
Next, let's consider the possibilities for the number of 3s in each group. Since 3^1 = 3, we can have either 1 or 2 groups with 3 students each (2^3 * 3^1 / 3^1 = 2^3 = 1 group of 3).
Combining these possibilities, we have the following ways to divide the class:
1. 3 groups of 2 students each
2. 2 groups of 3 students each
Therefore, Mrs. Garcia can divide the class into groups in two different ways based on prime factorization.