Work out cash denomination breakdown instantly with clear inputs, formula shown and shareable results.
Greedy denomination breakdown takes the largest note or coin that fits, repeatedly, until nothing remains. For standard note and coin systems this always produces the minimum number of pieces, which is why tills and cash machines use exactly this method.
Greedy change
repeatedly take the largest denomination not exceeding the remainder
For real-world currency systems, yes. It can fail for artificial sets — with coins of 1, 3 and 4, making 6 greedily gives 4+1+1 instead of 3+3.
Because a remainder finer than the smallest available piece cannot be paid, so the total must be rounded before breaking it down.