# Thread: 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$bill is added 11. The prime factorization of 540 is 2 X 2 X 3. Find the number of divisors of 12 other than 1 by finding all combination of these numbers The prime factorization of 540 is 2 X 2 X 3 X 3 X 3 X 5. Find the other numbers of divisor of 540. Other then 1 2. Originally Posted by Mr. Edward 11. The prime factorization of 12 is 2 X 2 X 3. Find the number of divisors of 12 other than 1 by finding all combination of these numbers The prime factorization of 540 is 2 X 2 X 3 X 3 X 3 X 5. Find the other numbers of divisor of 540. Other then 1 If$\displaystyle p_1,\ ..,\ p_n$are the distinct prime factors of$\displaystyle N$, with multiplicities$\displaystyle k_1,\ ..,\ k_n$(number of times they appear in the prime factorisation of$\displaystyle N$), then any of the numbers:$\displaystyle l=p_1^{r_1}p_2^{r_2}..p_n^{r_n},\ r_i \in \{0,..,k_i \}$is a factor of$\displaystyle N$and different combinations of the$\displaystyle r $'s give distinct factors. There are:$\displaystyle d(N)=\prod_{i=1}^n (k_i+1)$different combinations of the$\displaystyle r $'s, and so distinct factors of$\displaystyle N\$

RonL

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# divisor of 540

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