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# What is meant by quotient and remainder

2 ответов

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Some examples (because I'm not that good at explaining):
4 / 2 = 2
quotient: 2 (number of times it can be divided without overshooting)
remainder: 0 (it's a whole number)
10 / 3 = 3.33...
quotient: 3
remainder: 1 (the leftover of the "undershot" division)
3 / 5 = 0.6
quotient: 0 (divisor is greater than dividend)
remainder: 5
In Python there are operators which allow you to get the quotient and remainder of divisions:
"//" quotient operator
>>> 12 // 5
2
"%" remainder/modulo operator
>>> 12 % 5
3
There are lots of good examples in the internet (with pictures) it would definitely help to do more research to clarify it :)

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So quotient remainder theorem is a theorem from modular arithmetics.
The quotient remainder theorem says:
Given any integer A, and a positive integer B, there exist unique integers Q and R such that.
In other words you have
A= B * Q + R where 0 ≤ R < B
You can use this for make somes proves in modular arithmetic. Some direct
consequence is that you can have with this propertie is: if you can write a number
using
A= B * Q + R where 0 ≤ R < B
you can write in this form other form bellow too.
A mod B = R