There are 12 girls and 18 boys in a class. What is the largest number of groups they can be split into and have the same number of boys and girls on each team?
What are the common factors of 12 and 18?
12 it's 12!!! Hahaha
To find the largest number of groups that can be split with the same number of boys and girls on each team, we need to find the greatest common divisor (GCD) of 12 and 18.
Step 1: List all the divisors of both 12 and 18.
Divisors of 12: 1, 2, 3, 4, 6, 12
Divisors of 18: 1, 2, 3, 6, 9, 18
Step 2: Find the common divisors of 12 and 18.
Common divisors: 1, 2, 3, 6
Step 3: Identify the greatest common divisor.
Greatest common divisor: 6
Therefore, the largest number of groups that can be split with the same number of boys and girls on each team is 6.
To determine the largest number of groups they can be split into and have the same number of boys and girls on each team, we need to find the greatest common divisor (GCD) of the number of girls and boys.
In this case, we have 12 girls and 18 boys. To find the GCD, we can use the Euclidean algorithm.
The Euclidean algorithm states that to find the GCD of two numbers, we divide the larger number by the smaller number, then divide the remainder by the smaller number, and so on, until we obtain a remainder of zero. The last non-zero remainder is the GCD of the two numbers.
Let's apply the Euclidean algorithm to find the GCD of 12 and 18:
Step 1: Divide 18 by 12. The quotient is 1 and the remainder is 6.
Step 2: Divide 12 by 6. The quotient is 2 and the remainder is 0.
Since we obtained a remainder of zero, the GCD of 12 and 18 is 6.
Therefore, the largest number of groups they can be split into and have the same number of boys and girls on each team is 6.