Long Division Problem: Divide 518 by 7 Step-by-Step

To solve the problem of dividing 518 by 7, we'll perform long division:

1. Start with the first digit of the dividend, which is 5, in the hundreds place.

• $7$ does not go into $5$, so proceed to the next digit to make it 51.

2. Determine how many times $7$ goes into $51$ completely:

• $7 \times 7 = 49$, which is closest to 51 without exceeding it.
• Write $7$ as part of the quotient.
• Subtract $49$ from $51$, which leaves a remainder of $2$.

3. Bring down the next digit from the dividend, which is $8$, making the new number $28$.

4. Determine how many times $7$ goes into $28$ completely:

• $7 \times 4 = 28$, which equals 28.
• Write $4$ as the next digit of the quotient.
• Subtract $28$ from $28$, which leaves a remainder of $0$.

Since we reach a remainder of 0 after using all digits of the dividend, the division is exact. Therefore, the result is:

$74$. Thus, the correct answer is choice 3.