**An example.** Divmod combines two division operators. It performs an integral division and a modulo division. It returns a two-item pair (a tuple).

Tuple**Elements:** The first element is the result of the integral division. And the second is the modulo result.

**Usually:** You can compute these numbers with the "/" and "%" operators. This sometimes does not apply for floating-point numbers.

**Python program that uses divmod**
a = 12
b = 7*
# Call divmod.
*x = __divmod__(a, b)*
# The first part.
*print(x[0])*
# The second part (remainder).
*print(x[1])
**Output**
1
5

**Make change with divmod.** We can count coins with divmod. This method, make_change, changes "cents" into quarters, nickels, and cents. We repeatedly call divmod.

**Tip:** This approach cannot make change in all combinations. A recursive method is able to generate all possibilities.

Recursion**Result:** The program discovers that 81 cents can be made with five coins together. This logic applies to any currency.

**Python program that makes change with divmod**
def make_change(cents):*
# Use modulo 25 to find quarter count.
*parts = __divmod__(cents, 25)
quarters = parts[0]*
# Use modulo 5 on remainder to find nickel count.
*cents_remaining = parts[1]
parts = __divmod__(cents_remaining, 5)
nickels = parts[0]*
# Pennies are the remainder.
*cents_remaining = parts[1]*
# Display the results.
*print("Argument:", cents)
print("Quarters:", quarters)
print("Nickels:", nickels)
print("Pennies:", cents_remaining)*
# Test with 81 cents.
*make_change(81)
**Output**
('Argument:', 81)
('Quarters:', 3)
('Nickels:', 1)
('Pennies:', 1)

**Modulo.** Here we use the "%" symbol. Modulo computes the remainder of a division. The numbers are divided as normal, but the expression returns the amount left over.

**Tip:** Modulo is a good choice when an actual division is not needed. Otherwise, use divmod.

**Python program that uses modulo**
*# Input values.
*a = 12
b = 7*
# Use modulo operator.
*c = *a % b*
print(c)
**Output**
5

**Modulo in loops.** Sometimes loops need to vary their behavior once every few iterations. A modulo in an if-statement is ideal for this. We take action based on the index's value.

**Here:** We display whether each index in the for-loop is evenly divisible by 2, 3 and 4.

**Python program that uses modulo division in loop**
*# Loop over values from 0 through 9.
*__for__ i in range(0, 10):*
# Buildup string showing evenly divisible numbers.
*line = str(i) + ":"
if (i % 4) == 0:
line += " %4"
if (i % 3) == 0:
line += " %3"
if (i % 2) == 0:
line += " %2"*
# Display results for this line.
*print(line)
**Output**
0: %4 %3 %2
1:
2: %2
3: %3
4: %4 %2
5:
6: %3 %2
7:
8: %4 %2
9: %3

**Even, odd.** These methods test the parity of numbers. With even, all numbers are evenly divisible by 2. With odd, no numbers are evenly divisible by 2—a remainder of 1 or -1 is always left.

**Warning:** We cannot define odd() by testing for a remainder of 1. This will fail on negative numbers, which are validly odd numbers.

**Python program that tests for even, odd numbers**
def even(number):*
# Even numbers have no remainder when divided by 2.
*return (number % 2) == 0
def odd(number):*
# Odd numbers have 1 or -1 remainder when divided by 2.
*return (number % 2) != 0*
# Test even and odd methods.
*print("#", "Even?", "Odd?")
for value in range(-3, 3):
print(value, even(value), odd(value))
**Output**
('#', 'Even?', 'Odd?')
(-3, False, True)
(-2, True, False)
(-1, False, True)
(0, True, False)
(1, False, True)
(2, True, False)

**Divmod,** and its lower-level friend modulo, have many uses in programs. They are essential. We can make change, control loops, and test for specific number properties like parity.