How to Compute the Number/Denomination of Bills/Coins When Making Change

Whenever you pay in cash at a store, the cashier will make change so that the fewest number of bills and coins are used (unless you ask for certain denominations).

For instance, if your change due is $5.77, the cashier will give you 1 five-dollar bill, 3 quarters, and 2 pennies. That combination uses the fewest number of bills and coins. (In this case, 6 pieces of currency.)

The cashier could give you 5 one-dollar bills, 6 dimes, and 17 pennies to make $5.77, but this combination involves many more pieces of money.

To count the most efficient combination of bills and coins, you must divide the amount by the highest denomination bill, take the remainder, then divide the remainder by the next highest denomination and so on until you get down to pennies.

One example is worked out below; you can also use the convenient calculator on the left. Just enter the amount of money you want to break down into coins and bills and the calculator will output the most efficient arrangement.

Example:

Sara needs to pay her roommate $278.95 in cash, and she wants to use the fewest number of bills and coins. She does not want to use two-dollar bills or fifty-cent pieces.

The first step is to divide 278.95 by 100. This produces 2 with a remainder of 78.95, so she must use 2 hundred-dollar bills.

Next, she divides 78.95 by 50, which produces 1 with a remainder of 28.95. So she must use 1 fifty-dollar bill.

Next, divide 28.95 by 20, which gives 1 remainder 8.95. This means she uses 1 twenty-dollar bill.

Divide 8.95 by 5. This gives 1 remainder 3.95, so she uses 1 five-dollar bill.

Divide 3.95 by 1. This gives 3 remainder 0.95, so Sara uses 3 one-dollar bills

Now she must compute the coins needed to make 95 cents. Starting with quarters, she divides 95 by 25, which gives her 3 remainder 20. And so Sara uses 3 quarters. Finally, she divides 20 by 10, which gives her exactly 2. Thus, the last coins she uses are 2 dimes. The total of coins and bills she pays her roommate consists of:

2 hundred-dollar bills
1 fifty-dollar bill
1 twenty-dollar bill
1 five-dollar bill
3 one-dollar bills
3 quarters
2 dimes

© Had2Know 2010