Question

find the quotient and the remainder.
73 \overline{)49,965} \text{ r } \square

Explanation:

Step1: Divide 49965 by 73

We perform long division: \( 49965 \div 73 \).
First, we see how many times 73 goes into 499. \( 73\times6 = 438 \), \( 73\times7 = 511 \) (too big), so 6 times. Subtract \( 499 - 438 = 61 \).
Bring down the next digit (6) to make 616. \( 73\times8 = 584 \), \( 73\times9 = 657 \) (too big), so 8 times. Subtract \( 616 - 584 = 32 \).
Bring down the next digit (5) to make 325. \( 73\times4 = 292 \), \( 73\times5 = 365 \) (too big), so 4 times. Subtract \( 325 - 292 = 33 \).
So the quotient is \( 684 \) and the remainder is \( 33 \).

Step2: Verify

Check with \( \text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder} \).
\( 73\times684 + 33 = 73\times(600 + 80 + 4) + 33 = (73\times600)+(73\times80)+(73\times4)+33 = 43800 + 5840 + 292 + 33 = 43800+5840 = 49640; 49640 + 292 = 49932; 49932 + 33 = 49965 \), which matches the dividend.

Answer:

Quotient: \( 684 \), Remainder: \( 33 \)