Quotient-Remainder Theorem Calculator

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Given n = 985 and d = 43, demonstrate the quotient remainder theorem

The quotient-remainder theorem states that 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 - The integer quotient when n is divided by d:
From our long division calculator, q = 985 ÷ 43 = Floor(22.) = 22

Determine n mod d - the remainder when n is divided by d:
From our modulus calculator, we see that r = 985 mod 43 = 39

Quotient-Remainder Theorem:
n = dq + r
985 = (43)(22) + 39
985 = 946 + 39
985 = 985