# Quotient-Remainder Theorem Calculator

## Enter n and d

<-- Enter n
<-- Enter d

Given n = 15 and d = 20:
Show the quotient remainder theorem

## Quotient Remainder Definition

For positive integers n and d
n div d = q
n mod d = r <--> n = dq + r
and 0 ≤ r < d

## Determine n div d:

This is the integer quotient when n ÷ d
15 ÷ 20 = Floor(0.75) = 0

15 mod 20 = 15

## Quotient-Remainder Theorem:

n = dq + r
15 = (20)(0) + 15
15 = 0 + 15

15 = 15

### How does the Quotient-Remainder Theorem Calculator work?

Free Quotient-Remainder Theorem Calculator - Given 2 positive integers n and d, this displays the quotient remainder theorem.
This calculator has 2 inputs.

### What 3 formulas are used for the Quotient-Remainder Theorem Calculator?

q = n div d
r = n mod d
n = dq + r

For more math formulas, check out our Formula Dossier

### What 6 concepts are covered in the Quotient-Remainder Theorem Calculator?

integer
a whole number; a number that is not a fraction
...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...
modulus
the remainder of a division, after one number is divided by another.
a mod b
quotient
The result of dividing two expressions.
quotient-remainder theorem
When we divide A by B, Q is the quotient, R is the remainder
remainder
The portion of a division operation leftover after dividing two integers
theorem
A statement provable using logic