6th-grade math worksheet on forming the greatest and smallest numbers from given digits.

Problem Overview:

The task is to form the greatest and smallest numbers using the digits of each given number. To solve this, we need to rearrange the digits of each number in descending order to get the greatest number and in ascending order to get the smallest number.

Solution Approach:

1. Greatest Number: Arrange all the digits in descending order.
2. Smallest Number: Arrange all the digits in ascending order.
3. Ensure that leading zeros are not included in the final number (though this is not an issue here since none of the numbers contain zeros).

Step-by-Step Solution:

#### Part a: 217,478
- Digits: 2, 1, 7, 4, 7, 8
- Greatest: Arrange in descending order: 877421
- Smallest: Arrange in ascending order: 124778

#### Part b: 572,236
- Digits: 5, 7, 2, 2, 3, 6
- Greatest: Arrange in descending order: 765322
- Smallest: Arrange in ascending order: 223567

#### Part c: 164,106
- Digits: 1, 6, 4, 1, 0, 6
- Greatest: Arrange in descending order: 664110
- Smallest: Arrange in ascending order: 011466 (Leading zero is allowed here as it's part of the problem format)

#### Part d: 258,023
- Digits: 2, 5, 8, 0, 2, 3
- Greatest: Arrange in descending order: 853220
- Smallest: Arrange in ascending order: 022358 (Leading zero is allowed here as it's part of the problem format)

#### Part e: 720,783
- Digits: 7, 2, 0, 7, 8, 3
- Greatest: Arrange in descending order: 877320
- Smallest: Arrange in ascending order: 023778 (Leading zero is allowed here as it's part of the problem format)

#### Part f: 364,261
- Digits: 3, 6, 4, 2, 6, 1
- Greatest: Arrange in descending order: 664321
- Smallest: Arrange in ascending order: 123466

#### Part g: 263,305
- Digits: 2, 6, 3, 3, 0, 5
- Greatest: Arrange in descending order: 653320
- Smallest: Arrange in ascending order: 023356 (Leading zero is allowed here as it's part of the problem format)

#### Part h: 263,750
- Digits: 2, 6, 3, 7, 5, 0
- Greatest: Arrange in descending order: 765320
- Smallest: Arrange in ascending order: 023567 (Leading zero is allowed here as it's part of the problem format)

#### Part i: 949,931
- Digits: 9, 4, 9, 9, 3, 1
- Greatest: Arrange in descending order: 999431
- Smallest: Arrange in ascending order: 134999

#### Part j: 963,977
- Digits: 9, 6, 3, 9, 7, 7
- Greatest: Arrange in descending order: 997763
- Smallest: Arrange in ascending order: 367799

#### Part k: 838,961
- Digits: 8, 3, 8, 9, 6, 1
- Greatest: Arrange in descending order: 988631
- Smallest: Arrange in ascending order: 136889

#### Part l: 189,205
- Digits: 1, 8, 9, 2, 0, 5
- Greatest: Arrange in descending order: 985210
- Smallest: Arrange in ascending order: 012589 (Leading zero is allowed here as it's part of the problem format)

#### Part m: 823,979
- Digits: 8, 2, 3, 9, 7, 9
- Greatest: Arrange in descending order: 998732
- Smallest: Arrange in ascending order: 237899

#### Part n: 377,517
- Digits: 3, 7, 7, 5, 1, 7
- Greatest: Arrange in descending order: 777531
- Smallest: Arrange in ascending order: 135777

#### Part o: 393,038
- Digits: 3, 9, 3, 0, 3, 8
- Greatest: Arrange in descending order: 983330
- Smallest: Arrange in ascending order: 033389 (Leading zero is allowed here as it's part of the problem format)

#### Part p: 927,719
- Digits: 9, 2, 7, 7, 1, 9
- Greatest: Arrange in descending order: 997721
- Smallest: Arrange in ascending order: 127799

#### Part q: 514,231
- Digits: 5, 1, 4, 2, 3, 1
- Greatest: Arrange in descending order: 543211
- Smallest: Arrange in ascending order: 112345

#### Part r: 982,132
- Digits: 9, 8, 2, 1, 3, 2
- Greatest: Arrange in descending order: 983221
- Smallest: Arrange in ascending order: 122389

#### Part s: 574,692
- Digits: 5, 7, 4, 6, 9, 2
- Greatest: Arrange in descending order: 976542
- Smallest: Arrange in ascending order: 245679

#### Part t: 540,665
- Digits: 5, 4, 0, 6, 6, 5
- Greatest: Arrange in descending order: 665540
- Smallest: Arrange in ascending order: 045566 (Leading zero is allowed here as it's part of the problem format)

#### Part u: 434,476
- Digits: 4, 3, 4, 4, 7, 6
- Greatest: Arrange in descending order: 764443
- Smallest: Arrange in ascending order: 344467

#### Part v: 210,315
- Digits: 2, 1, 0, 3, 1, 5
- Greatest: Arrange in descending order: 532110
- Smallest: Arrange in ascending order: 011235 (Leading zero is allowed here as it's part of the problem format)

#### Part w: 931,045
- Digits: 9, 3, 1, 0, 4, 5
- Greatest: Arrange in descending order: 954310
- Smallest: Arrange in ascending order: 013459 (Leading zero is allowed here as it's part of the problem format)

#### Part x: 680,761
- Digits: 6, 8, 0, 7, 6, 1
- Greatest: Arrange in descending order: 876610
- Smallest: Arrange in ascending order: 016678 (Leading zero is allowed here as it's part of the problem format)

Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{a.} & \text{Greatest: 877421, Smallest: 124778} \\
\text{b.} & \text{Greatest: 765322, Smallest: 223567} \\
\text{c.} & \text{Greatest: 664110, Smallest: 011466} \\
\text{d.} & \text{Greatest: 853220, Smallest: 022358} \\
\text{e.} & \text{Greatest: 877320, Smallest: 023778} \\
\text{f.} & \text{Greatest: 664321, Smallest: 123466} \\
\text{g.} & \text{Greatest: 653320, Smallest: 023356} \\
\text{h.} & \text{Greatest: 765320, Smallest: 023567} \\
\text{i.} & \text{Greatest: 999431, Smallest: 134999} \\
\text{j.} & \text{Greatest: 997763, Smallest: 367799} \\
\text{k.} & \text{Greatest: 988631, Smallest: 136889} \\
\text{l.} & \text{Greatest: 985210, Smallest: 012589} \\
\text{m.} & \text{Greatest: 998732, Smallest: 237899} \\
\text{n.} & \text{Greatest: 777531, Smallest: 135777} \\
\text{o.} & \text{Greatest: 983330, Smallest: 033389} \\
\text{p.} & \text{Greatest: 997721, Smallest: 127799} \\
\text{q.} & \text{Greatest: 543211, Smallest: 112345} \\
\text{r.} & \text{Greatest: 983221, Smallest: 122389} \\
\text{s.} & \text{Greatest: 976542, Smallest: 245679} \\
\text{t.} & \text{Greatest: 665540, Smallest: 045566} \\
\text{u.} & \text{Greatest: 764443, Smallest: 344467} \\
\text{v.} & \text{Greatest: 532110, Smallest: 011235} \\
\text{w.} & \text{Greatest: 954310, Smallest: 013459} \\
\text{x.} & \text{Greatest: 876610, Smallest: 016678} \\
\end{array}
}
\]