Question

Cindy wishes to arrange her coins into X piles, each consisting of the same number of coins, Y.
Each pile will have more than 1 coin and no pile will have all the coins. If there are 13 possible values for Y given all of the restrictions, what is the smallest number of coins she could have?
Please, help

Answer 1

i have read this now like five times, not exactly clear what it means, but i think you are being asked to find the smallest number with 13 factors

Answer 2

Let C be number of coins, then C = XY
If Y has 13 possible values, then same as C.

Answer 3

Yes, it is.

Answer 4

hmm good luck !

Answer 5

lets google "smallest number with 13 factors"

Answer 6

google says \(2^{12}\)

Answer 7

We should have a number with 14 factors, right? how can it be an odd number of factors?

Answer 8

oh, my bad. It has an odd number.

Answer 9

C is coins, C=XY , piles times number of coins in each pile. 13 ways to do it

Answer 10

why that answer is \(2^{12}\) is probably comprehensible, not clear to me right off the bat though

Answer 11

https://answers.yahoo.com/question/index?qid=20090511160501AAXfMNk

Answer 12

The answer is 144 but I don't know how to get it.

Answer 13

you are sure that is the answer? because \(2^{12}\) is way larger

Answer 14

yes,

Answer 15

144 = 2*2*2*2*3*3

Answer 16

2
4
8
16
3
9
2*3
2*9
4*3
4*9
8*3
8*9
16*3
16*9

Answer 17

so, if x =2, then y = 72 that is 2 piles, each pile has 72 coins
if x =4 , then y = 36, that is 4 piles, each pile has 36 coins.
so on and so on.
But how to settle down to 144?

Answer 18

@ganeshie8