Of course! Let's solve the division [tex]\( 17864 \div 44 \)[/tex] step by step.
1. Identify the initial digits:
- Start by looking at the first three digits of the number [tex]\(17864\)[/tex], which are [tex]\(178\)[/tex].
- Determine how many times [tex]\(44\)[/tex] can fit into [tex]\(178\)[/tex].
2. First division:
- [tex]\(44\)[/tex] goes into [tex]\(178\)[/tex] a certain number of times.
- To find this, we calculate [tex]\(178 \div 44\)[/tex], which gets us 4 because [tex]\(44 \times 4 = 176\)[/tex] and [tex]\(44 \times 5 = 220\)[/tex] (which is too large).
3. Subtract and bring down next digit:
- Subtract [tex]\(176\)[/tex] from [tex]\(178\)[/tex], resulting in a remainder: [tex]\(178 - 176 = 2\)[/tex].
- Bring down the next digit from [tex]\(17864\)[/tex], which is [tex]\(6\)[/tex]. This gives us [tex]\(26\)[/tex].
4. Second division:
- Determine how many times [tex]\(44\)[/tex] can fit into [tex]\(26\)[/tex].
- Since [tex]\(26\)[/tex] is less than [tex]\(44\)[/tex], [tex]\(44\)[/tex] does not fit into [tex]\(26\)[/tex], so we write [tex]\(0\)[/tex] in the quotient.
5. Bring down next digit:
- Bring down the next digit from [tex]\(17864\)[/tex], which is [tex]\(4\)[/tex]. This gives us [tex]\(260\)[/tex].
6. Third division:
- Determine how many times [tex]\(44\)[/tex] fits into [tex]\(260\)[/tex].
- Calculate [tex]\(260 \div 44\)[/tex], which is approximately 5. [tex]\(44 \times 5 = 220\)[/tex], so [tex]\(44\)[/tex] can fit into [tex]\(260\)[/tex] [tex]\(5\)[/tex] times.
7. Subtract:
- Subtract [tex]\(220\)[/tex] from [tex]\(260\)[/tex], resulting in a remainder: [tex]\(260 - 220 = 40\)[/tex].
8. Final remainder:
- Bring down the final digit [tex]\(4\)[/tex] from [tex]\(17864\)[/tex], making it [tex]\(400\)[/tex].
- Determine how many times [tex]\(44\)[/tex] fits into [tex]\(400\)[/tex].
- Calculate [tex]\(400 \div 44 = 9.09...\)[/tex], so a fit of 9.
- Multiplying, [tex]\(44 \times 9 = 396\)[/tex].
9. Final subtraction:
- Subtract [tex]\(396\)[/tex] from [tex]\(400\)[/tex], resulting in [tex]\(400 - 396 = 4\)[/tex].
Putting all the digits together, we get a quotient of 406 and a remainder of 0.
Therefore, the final answer is:
Quotient: 406, Remainder: 0.
