Forming Large Numbers
Forming large numbers from given digits is an important skill in Class 5 Maths. Students learn to arrange digits to create the largest and smallest possible numbers, with or without repeating digits. This skill builds a deep understanding of place value — the same digits arranged differently produce very different numbers.
For example, using the digits 5, 0, 3, 8, the largest 4-digit number is 8,530 and the smallest is 3,058 (not 0,358, because a number cannot start with 0).
What is Forming Large Numbers - Class 5 Maths (Large Numbers)?
Forming numbers means arranging given digits in a specific order to create a number with desired properties (largest, smallest, even, odd, etc.).
Rules for forming numbers:
- Largest number: Arrange digits in descending order (biggest digit first).
- Smallest number: Arrange digits in ascending order (smallest non-zero digit first). If 0 is among the digits, place it in the second position, not the first.
- A valid number cannot start with 0.
Forming Large Numbers Formula
Largest Number: Arrange digits in descending order
Smallest Number: Arrange digits in ascending order (0 goes after the first non-zero digit)
Solved Examples
Example 1: Example 1: Forming largest and smallest 4-digit numbers
Problem: Using digits 7, 2, 9, 4 (each once), form the largest and smallest 4-digit numbers.
Solution:
Largest: Arrange in descending order: 9, 7, 4, 2 → 9,742
Smallest: Arrange in ascending order: 2, 4, 7, 9 → 2,479
Example 2: Example 2: Forming numbers when 0 is included
Problem: Using digits 6, 0, 3, 1, form the largest and smallest 4-digit numbers.
Solution:
Largest: Descending: 6, 3, 1, 0 → 6,310
Smallest: Ascending would give 0, 1, 3, 6 → but 0136 is not valid.
Place the smallest non-zero digit (1) first, then 0, then remaining in ascending order: 1, 0, 3, 6 → 1,036
Example 3: Example 3: Forming a 6-digit number
Problem: Using digits 5, 8, 0, 2, 4, 7 (each once), form the largest and smallest 6-digit numbers.
Solution:
Largest: Descending: 8, 7, 5, 4, 2, 0 → 8,75,420
Smallest: Ascending: 0, 2, 4, 5, 7, 8 → cannot start with 0.
Place 2 first, then 0: 2, 0, 4, 5, 7, 8 → 2,04,578
Example 4: Example 4: Forming the largest 7-digit number
Problem: Using digits 3, 9, 1, 0, 5, 7, 6 form the largest 7-digit number.
Solution:
Descending order: 9, 7, 6, 5, 3, 1, 0 → 97,65,310
Example 5: Example 5: Forming numbers with repeated digits
Problem: Using digits 3, 3, 0, 5, 5, form the largest and smallest 5-digit numbers.
Solution:
Largest: Descending: 5, 5, 3, 3, 0 → 55,330
Smallest: Ascending: 0, 3, 3, 5, 5 → cannot start with 0.
Place 3 first, then 0: 3, 0, 3, 5, 5 → 30,355
Example 6: Example 6: Forming an even number
Problem: Using digits 1, 5, 8, 3, form the largest 4-digit even number.
Solution:
Step 1: For an even number, the ones digit must be even. The only even digit is 8.
Step 2: Fix 8 at the ones place. Arrange remaining (5, 3, 1) in descending order for the other places.
Step 3: 5, 3, 1, 8 → 5,318
Example 7: Example 7: Forming an odd number
Problem: Using digits 2, 6, 4, 7, form the smallest 4-digit odd number.
Solution:
Step 1: For an odd number, the ones digit must be odd. The only odd digit is 7.
Step 2: Fix 7 at the ones place. Arrange remaining (2, 4, 6) in ascending order.
Step 3: 2, 4, 6, 7 → 2,467
Example 8: Example 8: Word problem — House numbers
Problem: Kavi's house is on a street where houses are numbered using the digits 1, 0, 5, 2, 8. What are the largest and smallest possible 5-digit house numbers?
Solution:
Largest: 8, 5, 2, 1, 0 → 85,210
Smallest: 1, 0, 2, 5, 8 → 10,258
Example 9: Example 9: Forming an 8-digit number
Problem: Using the digits 4, 0, 2, 7, 1, 8, 3, 5 (each once), form the smallest 8-digit number.
Solution:
Step 1: Ascending order: 0, 1, 2, 3, 4, 5, 7, 8
Step 2: Cannot start with 0. Place 1 first, then 0: 1, 0, 2, 3, 4, 5, 7, 8
Answer: 1,02,34,578
Key Points to Remember
- To form the largest number, arrange digits in descending order.
- To form the smallest number, arrange digits in ascending order with the smallest non-zero digit first.
- A number cannot begin with 0. If 0 is among the digits, swap it to the second position.
- For an even number, the ones digit must be 0, 2, 4, 6, or 8.
- For an odd number, the ones digit must be 1, 3, 5, 7, or 9.
- For numbers divisible by 5, the ones digit must be 0 or 5.
- When digits are repeated, treat each occurrence as a separate digit.
- The difference between the largest and smallest numbers formed from the same digits gives interesting number patterns.
Practice Problems
- Using digits 6, 3, 9, 1, 0 (each once), form the largest and smallest 5-digit numbers.
- Form the largest even 5-digit number using digits 7, 5, 3, 2, 9.
- Using digits 4, 0, 0, 8, 5, form the smallest 5-digit number.
- Form the largest and smallest 7-digit numbers using digits 2, 0, 5, 1, 9, 3, 7.
- Using digits 6, 6, 2, 2, 0, form the smallest odd 5-digit number.
- Arjun has digit cards 1, 4, 7, 0, 3, 8. Form the largest and smallest 6-digit numbers.
- Form the largest 6-digit number divisible by 5 using digits 3, 7, 0, 2, 9, 5.
Frequently Asked Questions
Q1. How do you form the largest number from given digits?
Arrange the digits in descending order (largest digit first). For example, from 3, 7, 1, 5, the largest number is 7,531.
Q2. How do you form the smallest number when 0 is one of the digits?
Arrange digits in ascending order, but since a number cannot start with 0, place the smallest non-zero digit first and 0 in the second position. From 0, 4, 2, 8, the smallest number is 2,048 (not 0,248).
Q3. Can a number start with zero?
No. A number cannot have 0 as its leftmost (leading) digit. For example, 0452 is not a valid 4-digit number — it would simply be 452, a 3-digit number.
Q4. How do you form the largest even number from given digits?
Place the largest even digit at the ones place. Arrange the remaining digits in descending order for the other places. If no even digit exists, you cannot form an even number.
Q5. What if digits are repeated?
Treat each occurrence as a separate digit. For example, from 3, 3, 5, 0, the largest number is 5,330 and the smallest is 3,035.
Q6. How many different numbers can be formed from given digits?
For n different digits, n! (n factorial) arrangements exist, but some may start with 0 and are invalid. For example, from 3 different digits, up to 3! = 6 numbers can be formed, minus those starting with 0.
Q7. How do you form a number divisible by 5?
The ones digit must be 0 or 5. Choose 0 or 5 for the ones place, then arrange the remaining digits as needed (descending for largest, ascending for smallest).
Q8. Is forming numbers important for Class 5 exams?
Yes. Questions about forming the largest and smallest numbers from given digits are common in Class 5 CBSE exams. They test understanding of place value and number sense.
Related Topics
- Numbers up to Lakhs
- Comparing Large Numbers (Grade 5)
- Place Value of Large Numbers
- Indian and International Number System (Grade 5)
- Reading and Writing Large Numbers
- Ordering Large Numbers (Grade 5)
- Rounding Large Numbers
- Estimation (Grade 5)
- Roman Numerals (I to M)
- Numbers up to Crores
- Number Names in Lakhs and Crores
- Expanded Form of Large Numbers
