Divisors

[Loki123]

The answer is 32. What am I missing??

 

[blamocur]

I would agree with your answer if the question was about prime divisors.

 

[Loki123]

I would agree with your answer if the question was about prime divisors.

what's the difference? i never heard that term before

 

[blamocur]

Divisors which are prime numbers.
For example, 12 has only two prime divisors, 2 and 3, but their product 6 is also a divisor, as well as 1 and 12 itself.

 

[Loki123]

Divisors which are prime numbers.
For example, 12 has only two prime divisors, 2 and 3, but their product 6 is also a divisor, as well as 1 and 12 itself.

how do I determine divisors for 401 and 501?

 

[topsquark]

how do I determine divisors for 401 and 501?

You already did in your own work! 401 is prime and 501 = 3 * 167.

-Dan

 

[Loki123]

You already did in your own work! 401 is prime and 501 = 3 * 167.

-Dan

but i need to get 32 divisors. i got way less

 

[blamocur]

but i need to get 32 divisors. i got way less

How many did you get?

 

[Loki123]

How many did you get?

5

 

[topsquark]

Does [imath]2 \times 5 = 10[/imath] divide [imath]\binom{2005}{2003}[/imath]?

-Dan

 

[JeffM]

2, 3, 5, 167, 401 are prime divisors

In addition, each product of two or more of the prime divisors is also a divisor as is 1.

 

[Loki123]

2, 3, 5, 167, 401 are prime divisors

In addition, each product of two or more of the prime divisors is also a divisor as is 1.

so i need to add
6,10, 234, 802, 15, 1203, 835, 1002, 2005

now i have 14

 

[blamocur]

Any subset of 5 number, including the empty and the full one, can be used to obtain a divisor, and since all prime divisors are different you get 32 subsets.

 

[Loki123]

Any subset of 5 number, including the empty and the full one, can be used to obtain a divisor, and since all prime divisors are different you get 32 subsets.

is there a mathematical way to do this? trying to think of all of them sounds inadequate

 

[blamocur]

is there a mathematical way to do this? trying to think of all of them sounds inadequate

The way I understand the problem you are not required to list all of them, just to figure out how many of them there are. And there is a mathematical expression for the total number of subsets of a finite set.

 

[Loki123]

The way I understand the problem you are not required to list all of them, just to figure out how many of them there are. And there is a mathematical expression for the total number of subsets of a finite set.

perhaps combinations, variations or permutation
however, i do not undestand how to use the formula in this case
what is my n, what is my k?

 

[blamocur]

perhaps combinations, variations or permutation

Neither. How many subsets are there in a set of 2 elements? 3 elements?

 

[Loki123]

Neither. How many subsets are there in a set of 2 elements? 3 elements?

is that 2^n formula

 

[blamocur]

is that 2^n formula

It is. I hope you understand why and not just making a lucky guess.

 

[Loki123]

It is. I hope you understand why and not just making a lucky guess.

i do. dw