Mrs Rahel has three classes . Each class has 28,42 and 56 students respectively. Mrs Rahel wants to divide each class into groups so that every group in every class has the same number of students and there are no students left over. What the maximum number of students Mrs Rahel can put into each group?
To find the maximum number of students Mrs Rahel can put into each group, we need to find the greatest common factor (GCF) of 28, 42, and 56.
First, we can find the prime factors of each number:
28 = 2 x 2 x 7
42 = 2 x 3 x 7
56 = 2 x 2 x 2 x 7
Then, we can identify the common factors:
2 x 7 = 14
Therefore, the maximum number of students Mrs Rahel can put into each group is 14. She can divide her first class into 2 groups of 14 students each, her second class into 3 groups of 14 students each, and her third class into 4 groups of 14 students each.
To find the maximum number of students that Mrs. Rahel can put into each group, we need to determine the greatest common divisor (GCD) of the number of students in each class.
Step 1: Find the GCD of 28, 42, and 56.
- The prime factorization of 28 is 2^2 * 7.
- The prime factorization of 42 is 2 * 3 * 7.
- The prime factorization of 56 is 2^3 * 7.
- The common factors are 2 and 7.
- The highest power of 2 is 2^2 = 4.
- The highest power of 7 is 7.
Step 2: Multiply the highest power of each common prime factor:
4 * 7 = 28.
Therefore, the maximum number of students Mrs. Rahel can put into each group is 28.
To find the maximum number of students that Mrs. Rahel can put into each group, we need to find the common factors of the number of students in each class (28, 42, and 56).
Step 1: Find the factors of each number.
- Factors of 28: 1, 2, 4, 7, 14, 28
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Step 2: Find the common factors.
The only common factor among all three numbers is 2 and 7.
Step 3: Find the maximum common factor.
Since we want to divide each class into groups with no students left over, we need to find the maximum number that divides all three numbers. In this case, the maximum common factor is 2.
Therefore, the maximum number of students that Mrs. Rahel can put into each group is 2.