In mathematics, writing multiples of a given number involves multiplying the given number by natural numbers. For example, to write the multiples of 30, we can simply add 0s in the unit’s place of the multiples of 3 since ten times of 3 is 30. Thus, if we know the multiples for 3, we can quickly write the multiples of 30.
It is interesting to recall that every number is a factor and the multiple of itself. Thus, 30 is a factor of 30, and 30 is a multiple of 30. Also, 30 is the largest factor of 30 and is the least multiple of 30. However, we can mark some differences between factors and multiples of the given number, which you can learn here. In this article, you will get the list of multiples of 30, along with examples.
Learn: Multiples
What are the Multiples of 30?
The multiples of 30 are 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, etc. These multiples are obtained when we multiply 30 by natural numbers, i.e. 1, 2, 3, …, 10, respectively.
Facts about Multiples of 30
- The difference between consecutive multiples of 30 is always equal to 30
- 30 × m = Multiple of 30; where m is an integer
- pth multiple of 30 = 30 × p
- Multiples of 30 are exactly divisible by 30 without leaving any remainder
For example, 120, 330, 420, 570 are all multiples of 30 for the following reasons.
Justification by Division | Justification by Multiplication | |
120 ÷ 30 = 4 {remainder = 0} | 30 × 4 = 120 | 30 is multiplied by 4 to get 120 |
330 ÷ 30 = 11 {remainder = 0} | 30 × 11 = 330 | 30 is multiplied by 11 to get 330 |
420 ÷ 30 = 14 {remainder = 0} | 30 × 14 = 420 | 30 is multiplied by 14 to get 420 |
570 ÷ 30 = 19 {remainder = 0} | 30 × 19 = 570 | 30 is multiplied by 19 to get 570 |
We can get the multiples through the repeated addition of a number as many times as required. Let’s see the first ten multiples of 30 by multiplication and adding the number repeatedly, which are tabulated below.
First 10 Multiples of 30 | |
---|---|
30 × 1 = 30 | 30 |
30 × 2 = 60 | 30 + 30 = 60 |
30 × 3 = 90 | 30 + 30 + 30 = 90 |
30 × 4 = 120 | 30 + 30 + 30 + 30 = 120 |
30 × 5 = 150 | 30 + 30 + 30 + 30 + 30 = 150 |
30 × 6 = 180 | 30 + 30 + 30 + 30 + 30 + 30 = 180 |
30 × 7 = 210 | 30 + 30 + 30 + 30 + 30 + 30 + 30 = 210 |
30 × 8 = 240 | 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 = 240 |
30 × 9 = 270 | 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 = 270 |
30 × 10 = 300 | 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 = 300 |
Multiples of 30 Table
Go through the table given below to learn the first 20 multiples of 30 along with the multiplication notation for each multiple.
Multiplication of 30 with numbers | Multiples of 30 |
30 × 1 | 30 |
30 × 2 | 60 |
30 × 3 | 90 |
30 × 4 | 120 |
30 × 5 | 150 |
30 × 6 | 180 |
30 × 7 | 210 |
30 × 8 | 240 |
30 × 9 | 270 |
30 × 10 | 300 |
30 × 11 | 330 |
30 × 12 | 360 |
30 × 13 | 390 |
30 × 14 | 420 |
30 × 15 | 450 |
30 × 16 | 480 |
30 × 17 | 510 |
30 × 18 | 540 |
30 × 19 | 570 |
30 × 20 | 600 |
The above table is quite similar to the multiplication table of 3 as the results are 10 times that table.
Difference between multiples and factors of 30
Some of the differences between multiples and factors of 30 are given in the below table.
Multiples of 30 | Factors of 30 |
Multiples of a number are n-times of the given number. Thus, multiples of 30 are in the form of 30n, where n is a natural number. | Factors of 30 are the numbers which when multiplied together, produce the original number 30. |
Every multiple of 30 is divisible by 30 without leaving any number. | Every factor of 30 is an exact divisor of it. |
Multiples of 30 are 30, 60, 90, 120, 150, etc. | Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30. |
Multiples of 30 are infinite since we can write an infinite number of multiples for a given number. | The number 30 has a finite number of factors, i.e. 8 factors. |
Click here to learn more about factors.
Get the Multiples of More Numbers Here
Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, etc.
Multiples of 36 are 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, etc.
Multiples of 40 are 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, etc.
Multiples of 42 are 42, 84, 126, 168, 210, 252, 294, 336, 378, 420, etc.
Multiples of 45 are 45, 90, 135, 180, 225, 270, 315, 360, 405, 450, etc.
Multiples of 50 are 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, etc.
Multiples of 60 are 60, 120, 180, 240, 300, 360, 420, 480, 540, 600, etc.
Video Lesson on Common Multiples
![](https://cdn1.byjus.com/wp-content/uploads/2022/04/Common-multiples-and-its-applications.jpg)
Examples on Multiple of 30
Example 1:
What are the multiples of 30 between 55 and 105?
Solution:
We know that the first five multiples of 30 are 30, 60, 90, 120, and 150.
Therefore, the multiples of 30 between 55 and 105 are 60 and 90.
Example 2:
Write the multiples of 30 and 48.
Solution:
The multiples of 30 are 30, 60, 90, 120, 150, 180, 210, 240,…
The multiples of 48 are 48, 96, 144, 192, 240, 288, 336, 384, 432,…
Example 3:
What are the common multiples of 30 and 40?
Solution:
Multiples of 30 are 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420, etc.
Multiples of 40 are 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, etc
Therefore, the common multiples of 30 and 40 are 120, 240, 360, etc.
To understand more about multiples of a number, visit byjus.com and get practice with more Maths concepts.
Frequently Asked Questions on Multiples of 30
What are the first five multiples of 30?
The first five multiples of 30 are 30, 60, 90, 120, and 150.
What are all the factors of 30?
All the factors of 30 include 1, 2, 3, 5, 6, 10, 15, and 30.
How do you write multiples of 30 in pairs?
Unlike factor pairs, we can write the multiples of 30 in pairs as given below:
30 × 1 = 30; (30, 1)
30 × 2 = 60; (30, 2)
30 × 3 = 90; (30, 3)
30 × 4 = 120; (30, 4)
30 × 5 = 150; (30, 5)
Is the number 30, a multiple of 2?
Yes, 30 is a multiple of 2 since 2 × 15 = 30, i.e. 2 times 15 is 30.
What are the first 30 multiples of 3?
The first 30 multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, and 90.
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