Let n represent the number that is the solution to the problem.

We know that four of the positive divisors of n are: 1, 21, 35 and n.

We will first find the remaining four positive divisors and then determine n.

Since 21 is a divisor of n and 21 = 3 *7, 3 and 7 must also be divisors of n.

Since 35 is a divisor of n and 35 = 5 *7, 5 must also be a divisor of n.

Since 3 is a divisor of n and 5 is a divisor of n, and since 3 and 5 have no common divisors, 3* 5 = 15 must also be a divisor n.

We have found all eight of the positive divisors of n. The positive divisors are 1, 3, 5, 7, 15, 21, 35 and n.

We now need to determine n.

From the list of divisors, we see that the prime factors of n are 3, 5 and 7 therefore n = 3*5 *7 = 105.