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.