Factors: all problems

What is the sum of the prime factors of 2010?

How many positive factors does 23,232 have?

On June 1, a group of students is standing in rows, with 15 students in each row. On June 2, the same group is standing with all of the students in one long row. On June 3, the same group is standing with just one student in each row. On June 4, the same group is standing with 6 students in each row. This process continues through June 12 with a different number of students per row each day. However, on June 13, they cannot find a new way of organizing the students. What is the smallest possible number of students in the group?

How many positive multiples of 1,001 have less than 15 factors?

Let $N = 34 \cdot 34 \cdot 63 \cdot 270$. What is the ratio of the sum of the odd divisors of $N$ to the sum of the even divisors of $N$?

Let $n = 2^{31} 3^{19}$. How many positive integer divisors of $n^2$ are less than $n$ but do not divide $n$?

For some positive integer $n$, the number $110n^3$ has $110$ positive integer divisors, including $1$ and the number $110n^3$. How many positive integer divisors does the number $81n^4$ have?

How many positive factors does the number 60 have?

Find the sum of factors of 320.

How many positive divisors of 2020 do not also divide 1010?

What is the sum of $\frac{1}{a}$ over all positive factors $a$ of the number 360?

A positive integer $q$ is the product of a prime number and a perfect square. Additionally, $q$ is the product of a different prime number and a perfect cube. What is the least possible value of $q$?

What is the greatest integer $k$ such that $80!$ is divisible by $45^k$?