Greatest smallest numbers from given digits

Class 3 Class 4 CBSE UP Board

🔢 Greatest & Smallest Numbers from Given Digits

Imagine you have some digit cards – 3, 7, 1, 5. What's the BIGGEST number you can make? What's the SMALLEST? This is like being a number architect! You arrange the digits in different orders to build the largest possible number or the smallest possible number. In this post, we'll learn the rules step by step, with many solved examples.

1. Rule for Greatest Number

📐 To make the greatest number:

Arrange the given digits in descending order (from largest to smallest).

Example: Digits 3, 7, 1, 5 → Descending order: 7, 5, 3, 1 → Greatest number = 7,531

2. Rule for Smallest Number

📗 To make the smallest number:

Arrange the given digits in ascending order (from smallest to largest).

Example: Digits 3, 7, 1, 5 → Ascending order: 1, 3, 5, 7 → Smallest number = 1,357

3. Special Rule: When Zero is Included

⚠️ Zero cannot be at the beginning of a number! (Because 0357 is just 357). So we need a special trick for the smallest number.

📘 For the smallest number with zero:

1. Arrange digits in ascending order.
2. Find the smallest non-zero digit and bring it to the front.
3. Place zero(s) right after it, then the remaining digits in ascending order.

🔍 Greatest number with 8,5,0,3? ▼

Descending order: 8,5,3,0 → 8,530

🔍 Smallest number with 8,5,0,3? ▼

Step 1: Ascending order: 0,3,5,8
Step 2: Smallest non-zero = 3, bring to front
Step 3: Place zero after it: 3,0, then 5,8 → 3,058

4. Solved Examples (Step-by-Step)

📌 Example 1: Digits 4, 2, 9, 6

Greatest number: Arrange in descending order: 9, 6, 4, 2 → 9,642

Smallest number: Arrange in ascending order: 2, 4, 6, 9 → 2,469

📌 Example 2: Digits 7, 1, 3, 8

Descending order: 8, 7, 3, 1 → Greatest = 8,731

Ascending order: 1, 3, 7, 8 → Smallest = 1,378

📌 Example 3: Digits 5, 0, 2, 9

Greatest: Descending order: 9, 5, 2, 0 → 9,520

Smallest: Ascending order: 0, 2, 5, 9 → smallest non-zero is 2, bring to front, then 0, then 5,9 → 2,059

📌 Example 4: Digits 3, 0, 0, 8

Greatest: Descending order: 8, 3, 0, 0 → 8,300

Smallest: Ascending order: 0, 0, 3, 8 → smallest non-zero = 3, bring to front, then zeros, then 8 → 3,008

📌 Example 5: Digits 4, 1, 8, 6, 2

Greatest: Descending order: 8, 6, 4, 2, 1 → 86,421

Smallest: Ascending order: 1, 2, 4, 6, 8 → 12,468

📌 Example 6: Digits 7, 0, 3, 5, 1

Greatest: Descending order: 7, 5, 3, 1, 0 → 75,310

Smallest: Ascending order: 0, 1, 3, 5, 7 → smallest non-zero = 1, bring to front, then 0, then 3,5,7 → 10,357

✏️ Practice Zone

Try all questions yourself. Then click to check your answers.

🟡 Class 3 Level (3-digit numbers)

Q1. Digits: 4, 2, 8 → Greatest? Smallest?
Q2. Digits: 7, 1, 5 → Greatest? Smallest?
Q3. Digits: 9, 3, 0 → Greatest? Smallest? (Watch the zero!)
Q4. Digits: 2, 6, 4 → Greatest? Smallest?

🔵 Class 4 Level (4-digit numbers)

Q5. Digits: 3, 7, 1, 5 → Greatest? Smallest?
Q6. Digits: 8, 4, 6, 2 → Greatest? Smallest?
Q7. Digits: 5, 0, 9, 3 → Greatest? Smallest?
Q8. Digits: 7, 2, 0, 8 → Greatest? Smallest?
Q9. Digits: 1, 3, 0, 0 → Greatest? Smallest? (Tricky!)

🟢 Challenge

Q10. Using digits 4, 1, 8, 6, 2 (five digits), find the greatest and smallest numbers.
Q11. Using digits 7, 0, 3, 5, 1, find the greatest and smallest.
Q12. Find the difference between the greatest and smallest numbers formed from digits 9, 2, 8, 1, 5.

🔑 Show Answer Key ▼

Q1. Greatest: 842, Smallest: 248
Q2. Greatest: 751, Smallest: 157
Q3. Greatest: 930, Smallest: 309
Q4. Greatest: 642, Smallest: 246
Q5. Greatest: 7,531, Smallest: 1,357
Q6. Greatest: 8,642, Smallest: 2,468
Q7. Greatest: 9,530, Smallest: 3,059
Q8. Greatest: 8,720, Smallest: 2,078
Q9. Greatest: 3,100, Smallest: 1,003
Q10. Greatest: 86,421, Smallest: 12,468
Q11. Greatest: 75,310, Smallest: 10,357
Q12. Greatest: 98,521, Smallest: 12,589, Difference = 85,932

📄 Practice Worksheet

Master forming greatest and smallest numbers with our 30-question worksheet. Includes digit cards, zero rule, and challenge puzzles.

📥 Get Practice Worksheet

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