You have divided by two-digit numbers already. Fluency means doing it reliably: estimate each digit, keep the places lined up, and check by multiplying.
Key idea
Work from the left. At each place: divide (how many times does the divisor fit?), multiply, subtract, bring down the next digit. Write a 0 in the quotient when the divisor does not fit.
Why it works
Long division is a fast way of taking away big equal groups. For $8,736 \div 24$: 300 groups of 24 use 7,200, leaving 1,536; 60 more groups use 1,440, leaving 96; 4 more groups use 96. That is $300 + 60 + 4 = 364$ groups. The algorithm does exactly these steps, writing each count in its own place.
Worked example: Four digits by two digits
Find $8,736 \div 24$.
- 24 does not fit in 8, so start with 87. $87 \div 24$: 3 times. $3 \times 24 = 72$; $87 - 72 = 15$.
- Bring down the 3: 153. $153 \div 24$: 6 times. $6 \times 24 = 144$; $153 - 144 = 9$.
- Bring down the 6: 96. $96 \div 24 = 4$. $4 \times 24 = 96$; nothing is left.
- Check: $364 \times 24 = 8,736$.
Answer: 364
Worked example: A zero in the quotient
Find $4,872 \div 24$.
- $48 \div 24 = 2$, with nothing left.
- Bring down the 7: 24 does not fit in 7, so write 0 in the quotient.
- Bring down the 2: 72. $72 \div 24 = 3$.
- Check: $203 \times 24 = 4,872$.
Answer: 203
Worked example: With a remainder
Find $6,040 \div 17$.
- $60 \div 17$: 3 times ($51$), 9 left.
- Bring down the 4: 94. $94 \div 17$: 5 times ($85$), 9 left.
- Bring down the 0: 90. $90 \div 17$: 5 times ($85$), 5 left.
- Check: $355 \times 17 + 5 = 6,035 + 5 = 6,040$.
Answer: 355, remainder 5
Common mistake
Skipping the 0 when the divisor does not fit. Without it, $4,872 \div 24$ comes out as 23. Quick check: estimate first. $4,800 \div 24 = 200$, so an answer near 23 is far too small.