7) Marco distributes 1260 stickers among all his friends, who are fewer than 100, giving each of them the same number of stickers and distributing them all. What is the maximum number of friends Marco can have?
(A) 70
(B) 84
(C) 90
(D) 94
(E) none of the above
7. The answer is $(\mathbf{C})$.

The number of Marco's friends must be a divisor of 1260, and therefore the maximum number of friends Marco can have is the largest divisor of 1260 that is also less than 100. The prime factorization of 1260 is

$$
1260=2^{2} \cdot 3^{3} \cdot 5 \cdot 7,
$$

and shows that $90=2 \cdot 3^{2} \cdot 5$ is a divisor of 1260 and no other number between 90 and 100 is. Therefore, 90 is the largest divisor of 1260 that is also less than 100.

[Problem proposed by G. Barbarino.]