Question

123 exercise books, 205 pencils and 82 erasers are distributed to a class. Each student gets the same number of each item. How many pencils do each student get?

Answer 1

5 pencils per student. Found by dividing total pencils by the common factor of pencils and erasers (41).

We can find out how many pencils each student gets by dividing the total number of pencils by the greatest common factor (GCD) of the number of pencils and the number of erasers. The GCD is the largest number that is a factor of both 205 and 82.

In other words, it is the number that both 205 and 82 can be divided by evenly with no remainder.

To find the GCD, we can use the Euclidean algorithm:

gcd(205, 82) = gcd(82, 205 % 82) = gcd(82, 41) = gcd(41, 41) = 41

Therefore, the GCD of 205 and 82 is 41. This means that each student gets 205 pencils / 41 = 5 pencils.

So the answer is 5