Given n = 985 and d = 43:

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

985 ÷ 43 = Floor(22.906976744186) = 22

Determine n mod d (remainder)

985 mod 43 = 39

Quotient-Remainder Theorem:

n = dq + r

985 = (43)(22) + 39

985 = 946 + 39

985 = 985

What is the Answer?

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?

integera whole number; a number that is not a fraction
...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...modulusthe remainder of a division, after one number is divided by another.
a mod bquotientThe result of dividing two expressions.quotient-remainder theoremWhen we divide A by B, Q is the quotient, R is the remainderremainderThe portion of a division operation leftover after dividing two integerstheoremA statement provable using logic

Example calculations for the Quotient-Remainder Theorem Calculator

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