3. The product of two natural numbers is 600000. What can be the maximum of their Greatest Common Divisor?
(A) 100
(B) 3000
(C) 1
(D) 200
(E) 600
Problem 3. The answer is (D).

The prime factorization of 600000 is $2^{6} \cdot 3 \cdot 5^{5}$. If the product of $a$ and $b$ is 600000, there will be a total of six factors of 2, five factors of 5, and one factor of 3 in the factorizations of $a$ and $b$. The 3 will therefore not appear in the factorization of the greatest common divisor, while the maximum number of factors of 2 and 5 will be achieved by distributing three factors of 2 to each number, and dividing the five factors of 5 by placing two on one side and three on the other. The maximum value of the greatest common divisor is therefore $2^{3} \cdot 5^{2}=200$

(Problem proposed by P. Francini)