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30 Solved + 20 Practice
GuidedPath Noida · Primary Maths · Worksheet
Greatest & Smallest Numbers
Form the greatest and smallest numbers from given digits — with an interactive Digit Arranger, tap-to-reveal answers, match the following and true/false. 30 fully solved + 20 interactive practice questions.
📋 Worksheet Contents:
📌 Solved questions show full step-by-step working with colour-coded digit chips. Practice sections are interactive — tap chips to select, place them in Greatest and Smallest slots, and check your answer instantly!
Solved Questions — Starter
Q1 to Q10 · No zeros · 3 and 4 digit numbers · Clear rule shown
Q1
Form the greatest and smallest 3-digit numbers using digits 3, 7, 1 (each once). Starter
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Solution
3
7
1
1
Greatest: arrange digits in descending order → 7, 3, 1 → 731.
2
Smallest: arrange digits in ascending order → 1, 3, 7 → 137.
7
3
1
Greatest = 731
1
3
7
Smallest = 137
✓ Greatest = 731 | Smallest = 137
Q2
Form the greatest and smallest 4-digit numbers using digits 5, 2, 8, 4 (each once). Starter
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Solution
52
84
1
Sort descending: 8>5>4>2 → Greatest = 8,542.
2
Sort ascending: 2<4<5<8 → Smallest = 2,458.
✓ Greatest = 8,542 | Smallest = 2,458
Q3
Form the greatest and smallest 3-digit numbers using digits 9, 4, 6. Starter
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Solution
1
Descending: 9, 6, 4 → 964.
2
Ascending: 4, 6, 9 → 469.
✓ Greatest = 964 | Smallest = 469
Q4
Digits: 1, 9, 3, 5. Form greatest and smallest 4-digit numbers. Starter
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Solution
1
Descending: 9, 5, 3, 1 → 9,531.
2
Ascending: 1, 3, 5, 9 → 1,359.
✓ Greatest = 9,531 | Smallest = 1,359
Q5
Digits: 7, 7, 3 (7 is repeated). Form greatest and smallest 3-digit numbers. Starter
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Solution
1
Descending: 7, 7, 3 → 773.
2
Ascending: 3, 7, 7 → 377.
✓ Greatest = 773 | Smallest = 377
Q6
Digits: 6, 2, 9, 1. Which arrangement gives the greatest 4-digit number? Starter
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Solution
1
For greatest: place largest digit in thousands place first. Sort descending: 9>6>2>1 → 9,621.
✓ Greatest = 9,621
Q7
Digits: 4, 8, 2. Which arrangement gives the smallest 3-digit number? Starter
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Solution
1
For smallest: place smallest digit in hundreds place. Sort ascending: 2<4<8 → 248.
✓ Smallest = 248
Q8
Digits: 5, 5, 5. What is the greatest and smallest number? Starter
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Solution
1
All digits are the same → only one possible number: 555.
✓ Greatest = Smallest = 555
Q9
Digits: 3, 1, 4, 1 (1 is repeated). Form greatest and smallest 4-digit numbers. Starter
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Solution
1
Descending: 4, 3, 1, 1 → 4,311.
2
Ascending: 1, 1, 3, 4 → 1,134.
✓ Greatest = 4,311 | Smallest = 1,134
Q10
Digits: 8, 6, 3, 9. Form both greatest and smallest 4-digit numbers. Starter
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Solution
1
Descending: 9, 8, 6, 3 → 9,863.
2
Ascending: 3, 6, 8, 9 → 3,689.
✓ Greatest = 9,863 | Smallest = 3,689
Solved Questions — Core Practice
Q11 to Q22 · Includes zeros · Zero rule · Word problems
⚠ The Zero Rule — Read Before Q11
When forming the smallest number with a zero digit — 0 can never be the first digit. Put the next smallest non-zero digit first, then place 0 second. Example: digits 0,3,5 → smallest = 305 (not 035).
Q11
Digits: 0, 3, 7. Form greatest and smallest 3-digit numbers. Core
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Solution
0
3
7
1
Greatest: descending → 7, 3, 0 → 730. (Zero goes last — fine.)
2
Smallest: cannot start with 0. Smallest non-zero digit = 3. So: 3, 0, 7 → 307.
7
3
0
Greatest = 730
3
0
7
Smallest = 307
✓ Greatest = 730 | Smallest = 307
Q12
Digits: 0, 5, 2, 8. Form greatest and smallest 4-digit numbers. Core
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Solution
0
5
2
8
1
Greatest: descending → 8, 5, 2, 0 → 8,520.
2
Smallest: cannot start with 0. Smallest non-zero = 2. So: 2, 0, 5, 8 → 2,058.
✓ Greatest = 8,520 | Smallest = 2,058
Q13
Digits: 0, 0, 4, 9. Form greatest and smallest 4-digit numbers. Core
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Solution
1
Greatest: 9, 4, 0, 0 → 9,400.
2
Smallest: cannot start with 0. Smallest non-zero = 4. So: 4, 0, 0, 9 → 4,009.
✓ Greatest = 9,400 | Smallest = 4,009
Q14
A student says the smallest number from digits 0, 6, 1 is 016. Is the student correct? Core
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Solution
1
016 is not a 3-digit number. A number cannot start with 0.
2
Smallest non-zero digit = 1. So: 1, 0, 6 → 106.
✓ Student is wrong. Correct smallest = 106.
Q15
Digits: 0, 7, 3, 5. Form greatest and smallest 4-digit numbers. Core
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Solution
1
Greatest: 7, 5, 3, 0 → 7,530.
2
Smallest: first digit = 3, then 0, then 5, 7 → 3,057.
✓ Greatest = 7,530 | Smallest = 3,057
Q16
A lock code uses digits 4, 9, 2, 6. What is the greatest possible code? What is the smallest? Core
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Solution
1
Greatest code: 9, 6, 4, 2 → 9,642.
2
Smallest code: 2, 4, 6, 9 → 2,469.
✓ Greatest code = 9,642 | Smallest code = 2,469
Q17
Digits: 0, 0, 0, 5. Form greatest and smallest 4-digit numbers. Core
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Solution
1
Greatest: 5, 0, 0, 0 → 5,000.
2
Smallest: only non-zero is 5 → 5 must lead: 5, 0, 0, 0 → 5,000.
✓ Greatest = Smallest = 5,000 (only one arrangement possible)
Q18
Digits: 3, 8, 0, 3 (3 repeated). Form greatest and smallest 4-digit numbers. Core
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Solution
1
Descending: 8, 3, 3, 0 → 8,330.
2
Smallest: first digit = 3, then 0, then 3, 8 → 3,038.
✓ Greatest = 8,330 | Smallest = 3,038
Q19
A shopkeeper has ₹ notes with digits 5, 0, 0, 0. What is the greatest and smallest amount these digits can represent? Core
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Solution
1
Only non-zero digit is 5. Greatest = smallest = 5,000.
✓ Amount = ₹5,000 (only one arrangement)
Q20
Digits: 1, 0, 8, 5. Form greatest and smallest 4-digit numbers. Core
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Solution
1
Greatest: 8, 5, 1, 0 → 8,510.
2
Smallest: first digit = 1, then 0, then 5, 8 → 1,058.
✓ Greatest = 8,510 | Smallest = 1,058
Q21
Digits: 2, 9, 0, 2 (2 repeated, with zero). Form greatest and smallest. Core
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Solution
1
Greatest: 9, 2, 2, 0 → 9,220.
2
Smallest: first digit = 2, then 0, 2, 9 → 2,029.
✓ Greatest = 9,220 | Smallest = 2,029
Q22
The digits of a 4-digit number are 6, 0, 4, 8. Ravi forms 6,048 and says it is the smallest number. Is he correct? Core
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Solution
1
Smallest non-zero digit = 4. Place 4 first, then 0, then 6, 8 → 4,068.
2
4,068 < 6,048. Ravi's number is not the smallest.
✓ Ravi is wrong. Correct smallest = 4,068.
Solved Questions — Challenge
Q23 to Q30 · Tricky zeros · Conditions · HOTs
Q23
Digits: 0, 0, 6, 3. Form greatest and smallest 4-digit numbers. Challenge
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Solution
1
Greatest: 6, 3, 0, 0 → 6,300.
2
Smallest: first = 3, then 0, 0, 6 → 3,006.
✓ Greatest = 6,300 | Smallest = 3,006
Q24
Using digits 7, 2, 5, 0, form the greatest even 4-digit number. (Last digit must be even.) Challenge
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Solution
1
Even digits available: 2, 0. For greatest, fix the largest even digit at the end.
2
Try last digit = 2: remaining 7, 5, 0 → arrange descending: 7, 5, 0 | end=2 → 7,502.
3
Try last digit = 0: remaining 7, 5, 2 → 7, 5, 2 | end=0 → 7,520. 7,520 > 7,502.
✓ Greatest even number = 7,520
Q25
Using digits 4, 9, 1, 6, what is the difference between the greatest and smallest 4-digit numbers formed? Challenge
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Solution
1
Greatest: 9, 6, 4, 1 → 9,641.
2
Smallest: 1, 4, 6, 9 → 1,469.
3
Difference = 9,641 − 1,469 = 8,172.
✓ Difference = 8,172
Q26
Digits: 0, 1, 9, 0. Form greatest and smallest 4-digit numbers. Challenge
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Solution
1
Greatest: 9, 1, 0, 0 → 9,100.
2
Smallest: non-zero digits are 9 and 1. Smallest non-zero = 1. So: 1, 0, 0, 9 → 1,009.
✓ Greatest = 9,100 | Smallest = 1,009
Q27
I am a 4-digit number. My digits are 3, 5, 7, 2. I am the greatest number that can be formed. What is my value? Challenge
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Solution
1
Descending: 7, 5, 3, 2 → 7,532.
✓ I am 7,532.
Q28
Using digits 0, 3, 7, 5, what is the sum of the greatest and smallest 4-digit numbers? Challenge
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Solution
1
Greatest: 7, 5, 3, 0 → 7,530.
2
Smallest: 3, 0, 5, 7 → 3,057.
3
Sum = 7,530 + 3,057 = 10,587.
✓ Sum = 10,587
Q29
How many different 3-digit numbers can be formed using digits 2, 5, 8 (each once)? List the greatest and smallest among them. Challenge
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Solution
1
All arrangements: 258, 285, 528, 582, 825, 852 → 6 numbers.
2
Greatest = 852. Smallest = 258.
✓ 6 numbers total. Greatest = 852 | Smallest = 258
Q30
Meena forms the smallest 4-digit number from digits 0, 4, 2, 8 as 2,048. Rohan says the smallest is 2,048 but Priya says it is 2,048. Who is correct? Show your working. Challenge
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Solution
1
Smallest non-zero digit = 2. First digit = 2.
2
Remaining: 0, 4, 8. Place 0 next (smallest), then 4, then 8 → 2, 0, 4, 8 = 2,048.
3
All three say 2,048 → all are correct!
✓ All three are correct. Smallest = 2,048.
Practice — Digit Arranger
P1 to P10 · Tap a digit chip to select it, then tap a G (greatest) or S (smallest) slot to place it. Check when done!
Tap a digit chip to select it (it glows). Then tap any G slot or S slot to place it. Tap a filled slot to remove and return the chip. Press Check to verify. Reveal All shows the correct answer.
P1
Digits: 4, 9, 2. Arrange to form greatest and smallest 3-digit numbers.
▼
P2
Digits: 7, 1, 5, 3. Arrange to form greatest and smallest 4-digit numbers.
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P3
Digits: 0, 5, 8. Arrange to form greatest and smallest 3-digit numbers. (Zero rule applies!)
▼
P4
Digits: 0, 6, 3, 9. Arrange to form greatest and smallest 4-digit numbers.
▼
P5
Digits: 8, 8, 3, 1 (8 repeated). Arrange to form greatest and smallest 4-digit numbers.
▼
P6
Digits: 0, 0, 4, 7. Arrange to form greatest and smallest 4-digit numbers.
▼
P7
Digits: 5, 2, 7, 9. Arrange to form greatest and smallest 4-digit numbers.
▼
P8
Digits: 0, 1, 8, 5. Arrange to form greatest and smallest 4-digit numbers.
▼
P9
Digits: 3, 3, 3, 9. Arrange to form greatest and smallest 4-digit numbers.
▼
P10
Digits: 0, 0, 1, 9. Arrange to form greatest and smallest 4-digit numbers. Challenge
▼
Practice — Match the Following
P11 to P14 · Tap a left item, then the correct right item
P11–12
Match each set of digits to the greatest number formed.
▼
9, 4, 6
5, 2, 8, 4
0, 7, 3, 5
0, 0, 4, 9
1, 9, 3, 5
964
8,542
7,530
9,400
9,531
P13–14
Match each set of digits to the smallest number formed. (Watch the zero rule!)
▼
3, 7, 1
0, 3, 7
0, 5, 2, 8
0, 0, 6, 3
1, 9, 3, 5
137
307
2,058
3,006
1,359
Practice — True or False
P15 to P20 · Tap TRUE or FALSE — instant feedback
P15 The greatest 3-digit number from digits 5, 1, 8 is 851.
TRUE
FALSE
P16 The smallest 3-digit number from digits 0, 4, 7 is 047.
TRUE
FALSE
P17 Using digits 9, 9, 9, the greatest and smallest numbers are the same.
TRUE
FALSE
P18 The greatest 4-digit number from digits 3, 0, 8, 5 is 8,530.
TRUE
FALSE
P19 The smallest 4-digit number from digits 0, 6, 2, 9 is 2,069.
TRUE
FALSE
P20 Using digits 1, 0, 0, 8 — the smallest 4-digit number is 0,018.
TRUE
FALSE
Answer Key — Quick Reference
Interactive sections self-check — key covers solved highlights
🔑 Show Answer Key
▼
Solved Q1–10 (Greatest / Smallest)
Q1: G=731, S=137 | Q2: G=8,542, S=2,458 | Q3: G=964, S=469
Q4: G=9,531, S=1,359 | Q5: G=773, S=377 | Q6: G=9,621
Q7: S=248 | Q8: G=S=555 | Q9: G=4,311, S=1,134 | Q10: G=9,863, S=3,689
Q11: G=730, S=307 | Q12: G=8,520, S=2,058 | Q13: G=9,400, S=4,009
Q14: S=106 (not 016) | Q15: G=7,530, S=3,057 | Q16: G=9,642, S=2,469
Q17: G=S=5,000 | Q18: G=8,330, S=3,038 | Q20: G=8,510, S=1,058
Q21: G=9,220, S=2,029 | Q22: S=4,068 (not 6,048)
Q23: G=6,300, S=3,006 | Q24: Greatest even=7,520
Q25: Diff=8,172 | Q26: G=9,100, S=1,009
Q27: 7,532 | Q28: Sum=10,587 | Q29: 6 numbers, G=852, S=258 | Q30: 2,048
P1: G=942, S=249 | P2: G=7,531, S=1,357 | P3: G=850, S=508
P4: G=9,630, S=3,069 | P5: G=8,831, S=1,388 | P6: G=7,400, S=4,007
P7: G=9,752, S=2,579 | P8: G=8,510, S=1,058 | P9: G=9,333, S=3,339 | P10: G=9,100, S=1,009
P15: True | P16: False | P17: True | P18: True | P19: True | P20: False
