#math trivia for #February19: #50 is the largest “coin” dividing into a 100-unit “dollar”. What are the other “coins” for this “dollar”?

— Burt Kaliski Jr. (@modulomathy) February 19, 2012

For the purposes of this problem, a “coin” should be taken as a a divisor of 100 that is smaller than 100. Even though 100 itself is a divisor (and there are “dollar coins” in circulation, after all), if 100 were included in the definition, then 50 wouldn’t be the largest. So we’ll focus on divisors smaller than 100, which are:

1 2 5 10 20 25 50 .

United States currency currently has five of these coins in circulation (1, 5, 10, 25, 50). Euro coins occur in six of the denominations (1, 2, 5, 10, 20, 50), all except the quarter.

Bonus questions for numismatists (I don’t know the answers; please add here as comments):

- Are there any currencies with a 100-unit dollar that have all seven of these coins?
- Any currencies with a different “dollar” that have coins for all possible divisors?
- Any currencies that have a coin that doesn’t divide the dollar?

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