Divide Large Numbers Using Python

Python allows you to perform the basic mathematical operations like addition, subtraction, multiplication, and division on large numbers as Python's integers are arbitrary-precision, hence there is no limit on their size.

• You can divide large numbers as you would normally do. But this has a lot of precision issues as such operations cannot be guaranteed to be precise, as it might slow down the language.
• Usually, dividing large numbers results in a floating-point number, which cannot be precise since Python's float can only accurately be represented up to 15-17 decimal digits.
• To overcome this issue, we can perform division operation using division operator (/), floor division operator, or decimal module.
  

Let us discuss each approach in detail with the help of examples -

Divide Large Numbers Using Division Operator

Two larger numbers can be divided using either the division operator (/) or the floor division operator (//). The division operator returns a float result, while the floor division operator (//) returns the largest integer less than or equal to the result (i.e., it performs integer division).

Example

In the example program below, we will use the basic division operator / (which gives float output) and // operator (which gives integer output):

a = 81434917259440465804
b = 12345678901234567890

# Floating-point division
res = a / b

# Integer division
res_int = a // b

print("Float division:", res)
print("Integer division:", res_int)

The output of the above code is as follows -

Float division: 6.596228357380733
Integer division: 6

Divide Large Numbers Using Decimal Module

The Decimal module provides support to return correctly rounded decimal floating-point arithmetic. You can use this module along with the getcontext() method to perform a division operation on a large number.

Example

The example program uses a decimal module to return a high-precision decimal value as output:

from decimal import Decimal, getcontext

getcontext().prec = 10  # set a precision
a = Decimal(81434917259440465804)
b = Decimal(12345678901234567890)
res = a / b
print("The quotient after diving two large numbers is equal to:", res)

The output of the above code is as follows -

The quotient after diving two large numbers is equal to: 6.596228357