How to Find the First 20 Multiples of 9 Easily
The concept of multiples of 9 plays a key role in mathematics and is widely applicable—whether you are solving school sums, competitive exam questions, or spotting number patterns in daily life. Understanding multiples of 9 makes calculations faster and boosts your confidence in topics like divisibility, factors, and number series.
What Is a Multiple of 9?
A multiple of 9 is any number you get by multiplying 9 by an integer (whole number). For example, 9, 18, 27, and 36 are multiples of 9 because they result from multiplying 9 × 1, 9 × 2, 9 × 3, and 9 × 4. You’ll find this concept applied in multiples of other numbers, divisibility rules, and word problems in math classes.
Key Formula for Multiples of 9
Here’s the standard formula: \( 9n \), where n is any integer (positive, negative, or zero). So, the sequence is: 9 × 0 = 0, 9 × 1 = 9, 9 × 2 = 18, and so on.
List of Multiples of 9 Up to 100
| n | 9 × n | Multiple of 9 |
|---|---|---|
| 1 | 9 × 1 | 9 |
| 2 | 9 × 2 | 18 |
| 3 | 9 × 3 | 27 |
| 4 | 9 × 4 | 36 |
| 5 | 9 × 5 | 45 |
| 6 | 9 × 6 | 54 |
| 7 | 9 × 7 | 63 |
| 8 | 9 × 8 | 72 |
| 9 | 9 × 9 | 81 |
| 10 | 9 × 10 | 90 |
To go up to 100, just continue skip counting by 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99.
How to Check if a Number is a Multiple of 9
There’s a simple divisibility rule for 9: If the sum of the digits of a number is itself a multiple of 9, then the whole number is a multiple of 9. Let’s look at some examples:
1. Check 63: 6 + 3 = 9 → Yes, 63 is divisible by 9.
2. Check 125: 1 + 2 + 5 = 8 → No, 125 is not a multiple of 9.
3. Check 99: 9 + 9 = 18; 1 + 8 = 9 → Yes, 99 is divisible by 9.
Step-by-Step Illustration
- Pick an integer n (for example, n = 7)
Multiply by 9: 9 × 7 = 63 - To check if 63 is a multiple of 9:
Sum digits: 6 + 3 = 9. Since 9 is a multiple of 9, 63 is a multiple of 9.
Speed Trick or Vedic Shortcut
Here’s a quick shortcut for mental math: The digits of every multiple of 9 add up to 9 or a multiple of 9. Also, in the 9 times table, the tens digit increases by 1 while the unit digit decreases by 1. For example: 9, 18, 27, 36... (units: 9,8,7,6...; tens: 0,1,2,3...)
Example Trick: Want to know the 12th multiple of 9?
1. Multiply: 9 × 12 = 108
2. Check: 1 + 0 + 8 = 9 (always adds to 9!)
Shortcuts like this are great for school quizzes, mental math, and competitive exam tricks taught in Vedantu live classes.
Try These Yourself
- Write the first five multiples of 9.
- Check if 72 is a multiple of 9 using the digit sum rule.
- Find all multiples of 9 between 40 and 80.
- List three numbers that are not multiples of 9 but are multiples of 3.
Frequent Errors and Misunderstandings
- Mixing up "factors" and "multiples". Remember: Multiples are bigger than or equal to the number; factors are smaller or equal.
- Forgetting to start checking from 9 (not 1) as the first positive multiple of 9.
- Using fractions or decimals as multiples. Only whole numbers!
Relation to Other Concepts
The idea of multiples of 9 connects closely with factors of 9, divisibility rules, and multiples of 6 and other numbers. It’s also useful when learning about LCM and HCF and solving word problems involving grouping, patterns, and series.
Classroom Tip
A quick way to remember multiples of 9 is to use the 9 times table—write the tens digit in order (0 to 9) and the ones digit in reverse order (9 to 0): 09, 18, 27, 36, 45, 54, 63, 72, 81, 90. Vedantu’s teachers use this simple trick for rapid recall and confidence in live online classes.
We explored multiples of 9—from definition, formula, examples, error checks, tricks, and links to other topics. Keep practicing with Vedantu to master math patterns, calculations, and problem-solving skills around multiples and factors.
Related Vedantu pages:
Multiples of 6 |
Factors of 9 |
Divisibility Rules |
LCM and HCF |
Multiplication Tricks
FAQs on Multiples of 9 in Maths: Definition, Examples & Patterns
1. What are the first 10 multiples of 9?
The first ten multiples of 9 are obtained by multiplying 9 by the integers 1 through 10: 9, 18, 27, 36, 45, 54, 63, 72, 81, and 90. These are the products of 9 and each consecutive whole number.
2. How do you check if a number is a multiple of 9?
To determine if a number is a multiple of 9, use the divisibility rule for 9: Add all the digits of the number. If the sum is divisible by 9 (meaning the sum is a multiple of 9), then the original number is also a multiple of 9. For example, let's check 729: 7 + 2 + 9 = 18. Since 18 is divisible by 9 (18 = 9 x 2), 729 is a multiple of 9.
3. Are all multiples of 9 also multiples of 3?
Yes, all multiples of 9 are also multiples of 3. This is because 9 is a multiple of 3 (9 = 3 x 3). If a number is divisible by 9, it will always be divisible by 3 as well.
4. What is the difference between multiples and factors of 9?
Multiples of 9 are numbers obtained by multiplying 9 by any integer (whole number). Factors of 9 are numbers that divide 9 without leaving a remainder. For example, multiples of 9 include 9, 18, 27, 36... while factors of 9 are 1, 3, and 9.
5. Can you give a list of multiples of 9 up to 1000?
A complete list up to 1000 would be lengthy, but you can easily generate it by multiplying 9 by consecutive integers. The multiples of 9 up to 100 are: 9, 18, 27, ..., 99. To find larger multiples, continue this pattern: 9 x 11 = 99, 9 x 12 = 108 and so on, up to 9 x 111 = 999.
6. What are the common multiples of 9 and 12?
Common multiples of 9 and 12 are numbers that are multiples of both 9 and 12. To find them, list the multiples of each number: Multiples of 9: 9, 18, 27, 36, 45, 54, 72, 81, 90, 99, 108... Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108... The common multiples include 36, 72, 108, and so on. The least common multiple (LCM) is 36.
7. What is the largest multiple of 9 less than 1000?
The largest multiple of 9 less than 1000 is 999 (9 x 111).
8. Is zero a multiple of 9?
Yes, zero is considered a multiple of 9. Any integer multiplied by 9 results in 0. Since 9 x 0 = 0, zero is a multiple of 9.
9. How are multiples of 9 used in real-world applications?
Multiples of 9 appear in various applications, including: Divisibility checks (as described above), pattern recognition in math problems, and error detection in some systems (like ISBN numbers). The divisibility rule is a practical tool for quickly assessing if a number is a multiple of 9.
10. What is the relationship between multiples of 9 and their digit sums?
The sum of the digits of any multiple of 9 will also be a multiple of 9. This is the basis of the divisibility rule for 9. For instance, consider the multiple 54. The sum of its digits is 5 + 4 = 9, which is a multiple of 9.
11. Can multiples of 9 be negative?
Yes, multiples of 9 can be negative. If you multiply 9 by a negative integer, the result will be a negative multiple of 9. For example, 9 x -2 = -18. -18 is a negative multiple of 9.
