in a lunch room 36 fifth graders and 27 fourth graders are siting in equal groups. all the students in each group are in the same grade. what is the greatest number of students that can be in each group?
What is the largest number that divides into 36 and 27 evenly?
To find the greatest number of students that can be in each group, we need to find the greatest common divisor (GCD) of the two numbers: 36 and 27.
First, let's find the factors of both numbers:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 27: 1, 3, 9, 27
Now, let's find the greatest common divisor (GCD) of 36 and 27, which is the largest number that divides evenly into both:
Common factors of 36 and 27: 1, 3, 9
Since we want to find the greatest number of students that can be in each group, the GCD of 36 and 27 is 9.
Therefore, the greatest number of students that can be in each group is 9.
To find the greatest number of students that can be in each group, we need to find the greatest common divisor (GCD) of 36 and 27. The GCD is the largest number that divides both numbers evenly.
One way to find the GCD is by listing the factors of the two numbers and finding the largest common factor. Another approach is to use the Euclidean algorithm.
Let's use the Euclidean algorithm:
1. Divide 36 by 27: 36 ÷ 27 = 1 remainder 9.
2. Divide 27 by 9: 27 ÷ 9 = 3 remainder 0.
Since the remainder is 0, we have found that the GCD of 36 and 27 is 9. This means that the greatest number of students that can be in each group is 9.