# Math Help - number of divisors

1. ## number of divisors

7a) How many different sums of money can be made from a 2$bill, a 5$ bill and a 10$bill b) How many different sums of money can be made from the bills in a as well as one more 10$ bill
c) Why does the situation become much more complicated if another 5\$ bill is added

11. The prime factorization of 540 is 2 X 2 X 3. Find the number of divisors of 12 other than 1 by finding all combination of these numbers

The prime factorization of 540 is 2 X 2 X 3 X 3 X 3 X 5. Find the other numbers of divisor of 540. Other then 1

2. Originally Posted by Mr. Edward
11. The prime factorization of 12 is 2 X 2 X 3. Find the number of divisors of 12 other than 1 by finding all combination of these numbers

The prime factorization of 540 is 2 X 2 X 3 X 3 X 3 X 5. Find the other numbers of divisor of 540. Other then 1
If $p_1,\ ..,\ p_n$ are the distinct prime factors of $N$, with multiplicities $k_1,\ ..,\ k_n$ (number of times they appear in the prime factorisation of $N$), then any of the numbers:

$l=p_1^{r_1}p_2^{r_2}..p_n^{r_n},\ r_i \in \{0,..,k_i \}$

is a factor of $N$ and different combinations of the $r$'s give distinct factors.

There are:

$d(N)=\prod_{i=1}^n (k_i+1)$

different combinations of the $r$'s, and so distinct factors of $N$

RonL