Multiples of a Number
Multiples are the products we get when we multiply a number by 1, 2, 3, 4, and so on. They are the numbers that appear in a multiplication table.
Understanding multiples is essential for skip counting, finding common multiples, computing LCM, and recognising number patterns in Class 4.
What is Multiples of a Number - Class 4 Maths (Factors and Multiples)?
A multiple of a number is the result of multiplying that number by any whole number (1, 2, 3, 4, ...).
For example, multiples of 5 are: 5, 10, 15, 20, 25, 30, ...
Multiple of n = n × 1, n × 2, n × 3, n × 4, ...
Key fact: A number has infinitely many multiples (they never end).
Types and Properties
Properties of multiples:
- Every number is a multiple of itself (n × 1 = n).
- Every number is a multiple of 1.
- The smallest multiple of any number is the number itself.
- Multiples go on forever (they are infinite).
- 0 is a multiple of every number (n × 0 = 0).
Solved Examples
Example 1: Example 1: Listing Multiples
Problem: Write the first 8 multiples of 6.
Solution:
6 × 1 = 6, 6 × 2 = 12, 6 × 3 = 18, 6 × 4 = 24
6 × 5 = 30, 6 × 6 = 36, 6 × 7 = 42, 6 × 8 = 48
Answer: First 8 multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48
Example 2: Example 2: Is This a Multiple?
Problem: Is 45 a multiple of 9?
Solution:
Check: 45 ÷ 9 = 5 (exact, remainder 0)
Since 9 × 5 = 45, yes, 45 is a multiple of 9.
Answer: Yes, 45 is a multiple of 9.
Example 3: Example 3: Not a Multiple
Problem: Is 38 a multiple of 7?
Solution:
38 ÷ 7 = 5 remainder 3 (not exact)
Since there is a remainder, 38 is not a multiple of 7.
Answer: No, 38 is not a multiple of 7.
Example 4: Example 4: Multiples on a Number Line
Problem: Show the multiples of 4 on a number line up to 24.
Solution:
0 — 4 — 8 — 12 — 16 — 20 — 24
Each jump is +4 (skip counting by 4).
Answer: Multiples of 4 up to 24: 4, 8, 12, 16, 20, 24
Example 5: Example 5: Multiples and Multiplication Table
Problem: The 7th multiple of 8 is ___.
Solution:
7th multiple of 8 = 8 × 7 = 56
Answer: The 7th multiple of 8 is 56.
Example 6: Example 6: Finding Which Multiple
Problem: 72 is the ___th multiple of 9.
Solution:
72 ÷ 9 = 8
So 72 = 9 × 8, making it the 8th multiple.
Answer: 72 is the 8th multiple of 9.
Example 7: Example 7: Multiples Between Two Numbers
Problem: List all multiples of 7 between 30 and 60.
Solution:
7 × 5 = 35, 7 × 6 = 42, 7 × 7 = 49, 7 × 8 = 56
(7 × 4 = 28 is below 30; 7 × 9 = 63 is above 60)
Answer: 35, 42, 49, 56
Example 8: Example 8: Word Problem (Skip Counting)
Problem: Aman saves ₹8 every week. After how many weeks will he have saved exactly ₹56?
Solution:
We need to find which multiple of 8 equals 56.
56 ÷ 8 = 7
Answer: After 7 weeks.
Example 9: Example 9: Even and Odd Multiples
Problem: Are all multiples of 4 even?
Solution:
Multiples of 4: 4, 8, 12, 16, 20, 24, ...
4 is even. Even × any number = even.
Answer: Yes, all multiples of 4 are even (because 4 itself is even).
Example 10: Example 10: Pattern in Multiples of 9
Problem: Find the first 10 multiples of 9. What pattern do you see in the digit sums?
Solution:
| Multiple | Value | Digit Sum |
|---|---|---|
| 9×1 | 9 | 9 |
| 9×2 | 18 | 9 |
| 9×3 | 27 | 9 |
| 9×4 | 36 | 9 |
| 9×5 | 45 | 9 |
| 9×6 | 54 | 9 |
| 9×7 | 63 | 9 |
| 9×8 | 72 | 9 |
| 9×9 | 81 | 9 |
| 9×10 | 90 | 9 |
Answer: The digit sum of every multiple of 9 is always 9.
Real-World Applications
Multiples are used in everyday life:
- Skip counting: Counting by 2s, 5s, 10s (e.g., counting coins).
- Time: Minutes in hours (multiples of 60), days in weeks (multiples of 7).
- Shopping: Total cost when buying multiple items of the same price.
- Scheduling: Events that happen every 3rd day, every 4th week, etc.
Key Points to Remember
- A multiple of a number is obtained by multiplying it by 1, 2, 3, 4, ...
- The smallest multiple (other than 0) is the number itself.
- Multiples are infinite — they go on forever.
- To check if a number is a multiple, divide — if the remainder is 0, it is a multiple.
- Multiples of even numbers are always even.
- Multiples of odd numbers alternate between odd and even.
- Factors and multiples are inverses: if 3 is a factor of 12, then 12 is a multiple of 3.
Practice Problems
- Write the first 10 multiples of 7.
- Is 84 a multiple of 6? How do you check?
- Find all multiples of 8 between 40 and 80.
- Priya counts by 9s starting from 9. What is the 12th number she says?
- Which of these numbers are multiples of 5: 35, 42, 55, 60, 73?
- Dev saves ₹12 every day. On which day will he have exactly ₹144?
- Is 100 a multiple of 3? Explain.
- The 15th multiple of 4 is ___.
Frequently Asked Questions
Q1. What is the difference between factors and multiples?
Factors are numbers that divide a given number exactly (they are smaller or equal). Multiples are obtained by multiplying the number (they are larger or equal). Factors are finite; multiples are infinite.
Q2. Is 0 a multiple of every number?
Yes. Since n × 0 = 0 for any number n, zero is technically a multiple of every number. However, when listing multiples, we usually start from the number itself (n × 1).
Q3. How do I check if a number is a multiple of another?
Divide the number by the other number. If the remainder is 0, it is a multiple. For example, 63 ÷ 7 = 9 (remainder 0), so 63 is a multiple of 7.
Q4. Do multiples ever end?
No. Multiples of any number go on forever. You can always find the next multiple by adding the number again. For example, multiples of 3: 3, 6, 9, 12, 15, ... never stop.
Q5. Are multiples of odd numbers always odd?
No. Multiples of odd numbers alternate between odd and even. For example, multiples of 3: 3 (odd), 6 (even), 9 (odd), 12 (even), ...
Q6. What is the relationship between skip counting and multiples?
Skip counting by a number produces its multiples. Counting by 5s gives: 5, 10, 15, 20, 25, ... — these are the multiples of 5.
Q7. How are multiples related to multiplication tables?
The multiplication table of a number IS the list of its multiples. The 6-times table (6, 12, 18, 24, 30, ...) lists the multiples of 6.
Q8. Is finding multiples in the NCERT Class 4 syllabus?
Yes. NCERT Class 4 Maths covers multiples through skip counting, patterns in multiplication tables, and exercises on identifying multiples.
