You are trying to distribute 566 ice creams and 183 cookies evenly to all of the students in a class. But you end up having 5 ice creams left and 4 cookies short. What is the maximum number of students in the class?
To find the maximum number of students in the class, we need to find a common factor of both the number of ice creams and the number of cookies that evenly divides both numbers.
First, let's find the factors of 566 (the number of ice creams) and 183 (the number of cookies).
The factors of 566 are: 1, 2, 283, and 566.
The factors of 183 are: 1, 3, 61, and 183.
Now, let's find the common factors of both numbers. The common factors are:
1
So, the only factor that divides both 566 and 183 evenly is 1.
Now we will subtract 5 (the number of leftover ice creams) from 566 and 4 (the number of missing cookies) from 183 to get the actual number of ice creams and cookies that were distributed evenly.
566 - 5 = 561 (number of distributed ice creams)
183 - 4 = 179 (number of distributed cookies)
Since we want the common factor to evenly divide both the number of ice creams and the number of cookies, we need to find a factor that divides both 561 and 179.
The factors of 561 are: 1, 3, 11, 17, 33, 51, 187, 561.
The factors of 179 are: 1, 179.
The only common factor of both 561 and 179 is 1.
Therefore, the maximum number of students in the class is 1, as there is no other common factor that evenly divides both the number of ice creams and the number of cookies.