Question
Mitchell has just moved to a new town and wants to share plates of baked goods with his neighbors. He has 39 cookies and 26 brownies to share, and wants to split them equally among the plates with no food left over. What is the greatest number of plates he can make to share?
Answers
GPT-4o mini
To find the greatest number of plates Mitchell can make with the cookies and brownies such that both are shared equally without any leftover, we need to calculate the greatest common divisor (GCD) of the number of cookies and brownies he has.
Mitchell has:
- 39 cookies
- 26 brownies
We will find the GCD of 39 and 26. We can achieve this using the Euclidean algorithm.
1. First, divide 39 by 26:
\[
39 \div 26 = 1 \quad \text{(with a remainder of 39 - 26 = 13)}
\]
2. Next, we now need to find the GCD of 26 and the remainder 13. We perform the division:
\[
26 \div 13 = 2 \quad \text{(with a remainder of 0)}
\]
Since we have reached a remainder of 0, the divisor in this step (which is 13) is the GCD.
So, the GCD of 39 and 26 is 13.
This means Mitchell can make a maximum of 13 plates, sharing the cookies and brownies equally among the plates.
To confirm, we can check how many cookies and brownies would go on each plate:
- For cookies: \( \frac{39}{13} = 3 \) cookies per plate
- For brownies: \( \frac{26}{13} = 2 \) brownies per plate
Thus, the greatest number of plates Mitchell can make is
\[
\boxed{13}
\]
Mitchell has:
- 39 cookies
- 26 brownies
We will find the GCD of 39 and 26. We can achieve this using the Euclidean algorithm.
1. First, divide 39 by 26:
\[
39 \div 26 = 1 \quad \text{(with a remainder of 39 - 26 = 13)}
\]
2. Next, we now need to find the GCD of 26 and the remainder 13. We perform the division:
\[
26 \div 13 = 2 \quad \text{(with a remainder of 0)}
\]
Since we have reached a remainder of 0, the divisor in this step (which is 13) is the GCD.
So, the GCD of 39 and 26 is 13.
This means Mitchell can make a maximum of 13 plates, sharing the cookies and brownies equally among the plates.
To confirm, we can check how many cookies and brownies would go on each plate:
- For cookies: \( \frac{39}{13} = 3 \) cookies per plate
- For brownies: \( \frac{26}{13} = 2 \) brownies per plate
Thus, the greatest number of plates Mitchell can make is
\[
\boxed{13}
\]