What is the 5th multiple of 9?
36
45
54
63
of 10
Multiples of 9 – 100+ List, Examples
Multiples of 9 – 100+ List, Examples
Multiples of 9 are numbers that result from multiplying 9 by integers. In mathematics, these numbers play a crucial role in understanding various concepts related to integers and multiplication. Each multiple of 9 is a product of 9 and another whole number, making them integral to number theory. Recognizing these multiples helps in identifying divisors and factors of numbers, aiding in simplification and problem-solving. Multiples of 9 are also used in various mathematical problems and applications, highlighting their significance in the study of mathematics.
What are Multiples of 9?
Multiples of 9 are numbers obtained by multiplying 9 with any integer. They form a sequence like 9, 18, 27, 36, and so on, where each number is a product of 9 and a whole number.
For example, 18, 45, 72 and 81 are all multiples of 9, 44 is not a multiple of 9 for the following reasons:
| Number | Reason | Remainder |
|---|---|---|
| 18 | 9 x 2 = 18 | 0 |
| 45 | 9 x 5 = 45 | 0 |
| 72 | 9 x 8 = 72 | 0 |
| 81 | 9 x 9 = 81 | 0 |
| 44 | 44 ÷ 9 ≠ integer value | 8 |
List of First 100 Multiples of 9 with Remainders
| Number | Reason | Remainder |
|---|---|---|
| 9 | 9 ÷ 9 = 1, which is an integer | 0 |
| 18 | 18 ÷ 9 = 2, which is an integer | 0 |
| 27 | 27 ÷ 9 = 3, which is an integer | 0 |
| 36 | 36 ÷ 9 = 4, which is an integer | 0 |
| 45 | 45 ÷ 9 = 5, which is an integer | 0 |
| 54 | 54 ÷ 9 = 6, which is an integer | 0 |
| 63 | 63 ÷ 9 = 7, which is an integer | 0 |
| 72 | 72 ÷ 9 = 8, which is an integer | 0 |
| 81 | 81 ÷ 9 = 9, which is an integer | 0 |
| 90 | 90 ÷ 9 = 10, which is an integer | 0 |
| 99 | 99 ÷ 9 = 11, which is an integer | 0 |
| 108 | 108 ÷ 9 = 12, which is an integer | 0 |
| 117 | 117 ÷ 9 = 13, which is an integer | 0 |
| 126 | 126 ÷ 9 = 14, which is an integer | 0 |
| 135 | 135 ÷ 9 = 15, which is an integer | 0 |
| 144 | 144 ÷ 9 = 16, which is an integer | 0 |
| 153 | 153 ÷ 9 = 17, which is an integer | 0 |
| 162 | 162 ÷ 9 = 18, which is an integer | 0 |
| 171 | 171 ÷ 9 = 19, which is an integer | 0 |
| 180 | 180 ÷ 9 = 20, which is an integer | 0 |
| 189 | 189 ÷ 9 = 21, which is an integer | 0 |
| 198 | 198 ÷ 9 = 22, which is an integer | 0 |
| 207 | 207 ÷ 9 = 23, which is an integer | 0 |
| 216 | 216 ÷ 9 = 24, which is an integer | 0 |
| 225 | 225 ÷ 9 = 25, which is an integer | 0 |
| 234 | 234 ÷ 9 = 26, which is an integer | 0 |
| 243 | 243 ÷ 9 = 27, which is an integer | 0 |
| 252 | 252 ÷ 9 = 28, which is an integer | 0 |
| 261 | 261 ÷ 9 = 29, which is an integer | 0 |
| 270 | 270 ÷ 9 = 30, which is an integer | 0 |
| 279 | 279 ÷ 9 = 31, which is an integer | 0 |
| 288 | 288 ÷ 9 = 32, which is an integer | 0 |
| 297 | 297 ÷ 9 = 33, which is an integer | 0 |
| 306 | 306 ÷ 9 = 34, which is an integer | 0 |
| 315 | 315 ÷ 9 = 35, which is an integer | 0 |
| 324 | 324 ÷ 9 = 36, which is an integer | 0 |
| 333 | 333 ÷ 9 = 37, which is an integer | 0 |
| 342 | 342 ÷ 9 = 38, which is an integer | 0 |
| 351 | 351 ÷ 9 = 39, which is an integer | 0 |
| 360 | 360 ÷ 9 = 40, which is an integer | 0 |
| 369 | 369 ÷ 9 = 41, which is an integer | 0 |
| 378 | 378 ÷ 9 = 42, which is an integer | 0 |
| 387 | 387 ÷ 9 = 43, which is an integer | 0 |
| 396 | 396 ÷ 9 = 44, which is an integer | 0 |
| 405 | 405 ÷ 9 = 45, which is an integer | 0 |
| 414 | 414 ÷ 9 = 46, which is an integer | 0 |
| 423 | 423 ÷ 9 = 47, which is an integer | 0 |
| 432 | 432 ÷ 9 = 48, which is an integer | 0 |
| 441 | 441 ÷ 9 = 49, which is an integer | 0 |
| 450 | 450 ÷ 9 = 50, which is an integer | 0 |
| 459 | 459 ÷ 9 = 51, which is an integer | 0 |
| 468 | 468 ÷ 9 = 52, which is an integer | 0 |
| 477 | 477 ÷ 9 = 53, which is an integer | 0 |
| 486 | 486 ÷ 9 = 54, which is an integer | 0 |
| 495 | 495 ÷ 9 = 55, which is an integer | 0 |
| 504 | 504 ÷ 9 = 56, which is an integer | 0 |
| 513 | 513 ÷ 9 = 57, which is an integer | 0 |
| 522 | 522 ÷ 9 = 58, which is an integer | 0 |
| 531 | 531 ÷ 9 = 59, which is an integer | 0 |
| 540 | 540 ÷ 9 = 60, which is an integer | 0 |
| 549 | 549 ÷ 9 = 61, which is an integer | 0 |
| 558 | 558 ÷ 9 = 62, which is an integer | 0 |
| 567 | 567 ÷ 9 = 63, which is an integer | 0 |
| 576 | 576 ÷ 9 = 64, which is an integer | 0 |
| 585 | 585 ÷ 9 = 65, which is an integer | 0 |
| 594 | 594 ÷ 9 = 66, which is an integer | 0 |
| 603 | 603 ÷ 9 = 67, which is an integer | 0 |
| 612 | 612 ÷ 9 = 68, which is an integer | 0 |
| 621 | 621 ÷ 9 = 69, which is an integer | 0 |
| 630 | 630 ÷ 9 = 70, which is an integer | 0 |
| 639 | 639 ÷ 9 = 71, which is an integer | 0 |
| 648 | 648 ÷ 9 = 72, which is an integer | 0 |
| 657 | 657 ÷ 9 = 73, which is an integer | 0 |
| 666 | 666 ÷ 9 = 74, which is an integer | 0 |
| 675 | 675 ÷ 9 = 75, which is an integer | 0 |
| 684 | 684 ÷ 9 = 76, which is an integer | 0 |
| 693 | 693 ÷ 9 = 77, which is an integer | 0 |
| 702 | 702 ÷ 9 = 78, which is an integer | 0 |
| 711 | 711 ÷ 9 = 79, which is an integer | 0 |
| 720 | 720 ÷ 9 = 80, which is an integer | 0 |
| 729 | 729 ÷ 9 = 81, which is an integer | 0 |
| 738 | 738 ÷ 9 = 82, which is an integer | 0 |
| 747 | 747 ÷ 9 = 83, which is an integer | 0 |
| 756 | 756 ÷ 9 = 84, which is an integer | 0 |
| 765 | 765 ÷ 9 = 85, which is an integer | 0 |
| 774 | 774 ÷ 9 = 86, which is an integer | 0 |
| 783 | 783 ÷ 9 = 87, which is an integer | 0 |
| 792 | 792 ÷ 9 = 88, which is an integer | 0 |
| 801 | 801 ÷ 9 = 89, which is an integer | 0 |
| 810 | 810 ÷ 9 = 90, which is an integer | 0 |
| 819 | 819 ÷ 9 = 91, which is an integer | 0 |
| 828 | 828 ÷ 9 = 92, which is an integer | 0 |
| 837 | 837 ÷ 9 = 93, which is an integer | 0 |
| 846 | 846 ÷ 9 = 94, which is an integer | 0 |
| 855 | 855 ÷ 9 = 95, which is an integer | 0 |
| 864 | 864 ÷ 9 = 96, which is an integer | 0 |
| 873 | 873 ÷ 9 = 97, which is an integer | 0 |
| 882 | 882 ÷ 9 = 98, which is an integer | 0 |
| 891 | 891 ÷ 9 = 99, which is an integer | 0 |
| 900 | 900 ÷ 9 = 100, which is an integer | 0 |
Read More About Multiples of 9
Important Notes
Step 1: Understanding Multiples
- Definition: A multiple of a number is the product of that number and an integer.
- Multiple of 9: It is a number that can be expressed as 9×n, where n is an integer.
Step 2: Recognizing Patterns in Multiples of 9
- Sum of Digits: The sum of the digits of any multiple of 9 is also a multiple of 9. For example, for 18, 1+8 = 9, and for 81, 8+1 = 9.
- Recurring Sequence: The last digits of multiples of 9 follow a pattern: 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, and then it repeats.
Step 3: List of First 10 Multiples of 9
- 9×1 = 9
- 9×2 = 18
- 9×3 = 27
- 9×4 = 36
- 9×5 = 45
- 9×6 = 54
- 9×7 = 63
- 9×8 = 72
- 9×9 = 81
- 9×10 = 90
Step 4: Properties and Divisibility Rules
- Divisibility Rule: A number is divisible by 9 if the sum of its digits is divisible by 9.
- Example: Check if 738 is a multiple of 9. Sum of digits: 7+3+8 = 18, and since 18 is divisible by 9, 738 is a multiple of 9.
Step 5: Applications and Examples
- Real-Life Application: Multiples of 9 can be used in various scenarios like dividing items into equal groups, solving mathematical problems, and understanding patterns in number systems.
- Example Problem: If you have 81 apples and want to divide them into groups of 9, each group will contain 81/9 = 9 apples.
Examples on Multiples of 9
Example 1: Small Multiple of 9
Multiple: 9
Calculation: 9×1 = 9
Explanation: The smallest multiple of 9 is 9 itself. This is because any number multiplied by 1 remains unchanged. Hence, 9×1 = 9.
Example 2: Larger Multiple of 9
Multiple: 54
Calculation: 9×6 = 54
Explanation: To find the sixth multiple of 9, you multiply 9 by 6. This gives us: 9×6 = 54 Therefore, 54 is a multiple of 9.
Example 3: Even Larger Multiple of 9
Multiple: 108
Calculation: 9×12 = 108
Explanation: For the twelfth multiple of 9, you multiply 9 by 12. This calculation results in: 9×12 = 108 Thus, 108 is another multiple of 9.
Summary of Multiples of 9
Here is a table listing some multiples of 9 for quick reference:
| Multiplier n | Multiple 9×n |
|---|---|
| 1 | 9 |
| 2 | 18 |
| 3 | 27 |
| 4 | 36 |
| 5 | 45 |
| 6 | 54 |
| 7 | 63 |
| 8 | 72 |
| 9 | 81 |
| 10 | 90 |
| 11 | 99 |
| 12 | 108 |
FAQs
What is a multiple of 9?
A multiple of 9 is any number that can be expressed as 9 times an integer. For example, 9, 18, and 27 are multiples of 9 because they can be written as 9×1, 9×2, and 9×3, respectively.
How do you determine if a number is a multiple of 9?
To determine if a number is a multiple of 9, add all the digits of the number together. If the sum is a multiple of 9, then the original number is also a multiple of 9. For instance, 243 is a multiple of 9 because 2+4+3 = 9, which is a multiple of 9.
Why are multiples of 9 significant in mathematics?
Multiples of 9 are significant because they form a unique and predictable pattern in mathematics. This pattern can help in learning and understanding multiplication and divisibility rules, and they also appear in various real-world contexts.
Can negative numbers be multiples of 9?
Yes, negative numbers can also be multiples of 9. For example, -9, -18, and -27 are multiples of 9 because they are the products of 9 and negative integers (-9×1, -9×2, -9×3).
How are multiples of 9 used in everyday life?
Multiples of 9 are used in various everyday scenarios, such as packaging products in groups of 9, scheduling events every 9 days, and creating designs that use a 9×9 grid pattern.
What is the smallest positive multiple of 9?
The smallest positive multiple of 9 is 9 itself. It is obtained by multiplying 9 by 1.
How can understanding multiples of 9 help in financial planning?
Understanding multiples of 9 can assist in financial planning by simplifying bulk purchasing decisions, structuring payment plans, and calculating discounts. For example, if a store offers a “buy 9, get 1 free” promotion, knowing multiples of 9 helps customers quickly determine the best deal.
Are there any interesting patterns in the multiples of 9?
Yes, multiples of 9 exhibit interesting patterns. For example, in the sequence of multiples of 9 (9, 18, 27, 36, …), the sum of the digits of each multiple eventually adds up to 9. This pattern helps in quick verification of multiples.
What role do multiples of 9 play in digital systems and technology?
In digital systems and technology, multiples of 9 can be used in algorithm design and data structures. For example, some algorithms may process data in blocks that are multiples of 9 for optimized performance.
Can multiples of 9 help in solving puzzles and games?
Yes, multiples of 9 are often used in puzzles and games. Sudoku, a popular number puzzle, uses a 9×9 grid. Recognizing multiples of 9 can also help in understanding and solving other numeric puzzles efficiently.
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Practice Test
Which of the following numbers is a multiple of 9?
52
63
77
85
of 10
What is the sum of the first 4 multiples of 9?
126
135
144
153
of 10
Which number is divisible by 9?
144
157
169
181
of 10
If x is a multiple of 9, which of the following could be the value of x?
98
105
119
132
of 10
What is the 8th multiple of 9?
72
81
90
99
of 10
Which number is not a multiple of 9?
54
72
88
108
of 10
What is the product of the 3rd and 4th multiples of 9?
486
567
648
729
of 10
If a number is a multiple of 9 and less than 100, which of the following is a possible number?
99
102
105
117
of 10
Find the smallest multiple of 9 that is greater than 50.
54
63
72
81
of 10