Divmod. Division and modulo division are related operations. With division, the result is stored in a single number. With modulo division, only the remainder is returned.
With divmod, a built-in operator, we separate the two result values in a division. We get both the whole number of times the division occurs, and the remainder.
An example. Divmod combines two division operators. It performs an integral division and a modulo division. It returns a two-item pair (a tuple).
Return The first element is the result of the integral division. And the second is the modulo result.
Info You can compute these numbers with the "/" and "%" operators. This sometimes does not apply for floating-point numbers.
a = 12
b = 7
# Call divmod.
x = divmod(a, b)
# The first part.
print(x[0])
# The second part (remainder).
print(x[1])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.
Result The program discovers that 81 cents can be made with five coins together. This logic applies to any currency.
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)('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.
# Input values.
a = 12
b = 7
# Use modulo operator.
c = a % b
print(c)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.
# 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)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.
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))('#', 'Even?', 'Odd?')
(-3, False, True)
(-2, True, False)
(-1, False, True)
(0, True, False)
(1, False, True)
(2, True, False)
Prime numbers. With primes, we cannot divide by any number except 1 and the number itself. In a for-loop, we can test for primes by using modulo division.
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.
Dot Net Perls is a collection of tested code examples. Pages are continually updated to stay current, with code correctness a top priority.
Sam Allen is passionate about computer languages. In the past, his work has been recommended by Apple and Microsoft and he has studied computers at a selective university in the United States.
This page was last updated on Jun 26, 2023 (edit).