Number theory › Divisors

Divisors and common divisors

Solve the first problem 18 problems

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1. Count positive factors of 1100 ●○○○○ 10 ptsHow many distinct positive factors does $1100$ have?
2. Nested divisor-count function ●○○○○ 10 ptsLet $\boxed{N}$ mean the number of positive whole number divisors of $N$. For example, $\boxed{3}=2$, because $3$ has two divisors, $1$ and $3$. Find the value of $\boxed{\boxed{11}\times\boxed{20}}$.
3. Divisors among 1 through 6 ●○○○○ 10 ptsHow many of the six integers 1 through 6 are divisors of the four-digit number 1452?
4. Greatest shared divisor of 90 and m ●●○○○ 20 ptsTwo numbers $90$ and $m$ share exactly three positive divisors. What is the greatest of these three common divisors?
5. Product of divisors of 100 ●●○○○ 20 ptsWhat is the product of the positive integer divisors of $100$?
6. Divisors of exactly one number ●●○○○ 20 ptsHow many natural numbers divide exactly one of 1080 and 1800, but not both?

More in Divisors

Divisors of special numbersExtremes of divisorsFactor pairsListing factorsNumber and product of divisorsNumbers with a given divisor countSums of divisors