On children's day, a teacher brought 63 erasers and 147 sweets to distribute out completely to her class. Each student receives the same number of erasers as each other, and the same number of sweets as each other. What is the most number of students in the class?

Details and assumptions

The erasers and sweets may not be split apart. Each student receives a whole number of erasers and sweets. For example, there cannot be 2 students in the class, who would receive 32.5 erasers each.

Factor each number.

I get the largest number as 21.

63 = 3*3*7

147 = 3*7*7

So, to divide the erasers evenly, the number of students must be
3,7,9,21
Similarly the divisors of 147 are
3,7,21,49

So, it looks like 21 is the maximum number that divides both 63 and 147.
Note that GCD(63,147) = 21

To find the most number of students in the class, we need to determine the factors of both 63 (erasers) and 147 (sweets).

The factors of 63 are: 1, 3, 7, 9, 21, and 63.

The factors of 147 are: 1, 3, 7, 21, 49, and 147.

Since each student receives the same number of erasers and sweets, the number of students must be a common factor of both 63 and 147.

The common factors of 63 and 147 are: 1, 3, 7, and 21.

However, we need to distribute all the erasers and sweets completely, which means we need to find the greatest common factor (GCF) of 63 and 147.

The GCF of 63 and 147 is 21.

Therefore, the most number of students in the class is 21, because each student would receive 3 erasers and 7 sweets.