A multiple of a natural number is the product of that natural number with another natural number.

In other words, to find a multiple of a natural number, you must multiply that number by another natural number.

Example: 10 is a multiple of 5 because 10 = 2 ×5

40 is a multiple of 5 because 40 = 5 × 8

4670 is a multiple of 5 because 4670 = 5 × 934

## Multiple of a natural number formula

The formula to find the multiple of a natural number is:

Multiple = Natural Number × Another Natural Number

In mathematical notation, you can represent this as:

Multiple = N × M

Where:

– “Multiple” is the result, which is a multiple of the natural number.

– “Natural Number” is the given natural number for which you want to find a multiple.

– “Another Natural Number” is any other natural number that you choose to multiply with the given natural number to find its multiple.

– “N” represents the given natural number.

– “M” represents the other natural number you choose for multiplication.

For example, if you want to find a multiple of 7, you can choose any other natural number, say 3, and use the formula:

Multiple = 7 × 3 = 21

So, 21 is a multiple of 7, and you can use this formula with different values of “M” to find various multiples of 7.

## Properties

**1- Zero (0) is a multiple of any natural number.**

0 × n = 0 for any n

Example: 0 = 0 × 37

**2- Every natural number is a multiple of 1.**

n = 1 × n

Example: 29 = 1 × 29

**3- Every natural number is a multiple of itself.**

n = n × 1

Example: 67 = 67 × 1

**4- The sum of two multiples of the same natural number is a multiple of that natural number.**

Example: 12 = 3 × 4 12 is a multiple of 3

18 = 3 × 6 18 is a multiple of 3

The sum of the multiples: 12 + 18 = 30

30 = 3 × 10 30 is a multiple of 3

**5- The difference between two multiples of the same natural number is a multiple of that natural number.**

Example: 36 = 3 × 12 36 is a multiple of 3

21 = 3 × 7 21 is a multiple of 3

The difference of the multiples: 36 – 21 = 15

15 = 3 × 5 15 is a multiple of 3

Note: A natural number has an infinite number of multiples.

### Multiples of 1

Multiples of 1 are relatively straightforward since any number multiplied by 1 remains the same. Therefore, the multiples of 1 are all the positive integers. In other words, every natural number is a multiple of 1.

1 × 1 = 1 1 × 2 = 2 1 × 3 = 3 1 × 4 = 4 1 × 5 = 5

### Multiples of 2

A multiple of 2 is any number that can be evenly divided by 2 without leaving a remainder. In other words, if you can divide a number by 2 and get a whole number as the result, then that number is a multiple of 2.

Examples of multiples of 2 include:

– 2

– 4

– 6

– 8

– 10

– 12

– 14

– 16

– 18

– 20

And so on. These numbers can all be divided by 2 to give whole numbers.

### Multiples of 3

A multiple of 3 is a number that can be divided by 3 without a remainder. For example, 3, 6, 9, 12, and 15 are all multiples of 3.

There are a few ways to determine if a number is a multiple of 3. One way is to simply divide the number by 3 and see if the remainder is 0. If the remainder is 0, then the number is a multiple of 3.

Another way to determine if a number is a multiple of 3 is to add up the digits of the number and see if the sum is divisible by 3. If the sum is divisible by 3, then the number is also divisible by 3. For example, the number 12 is a multiple of 3 because 1 + 2 = 3, and 3 is divisible by 3.

Here are some examples of multiples of 3:

- 3
- 6
- 9
- 12
- 15
- 18
- 21
- 24
- 27
- 30
- 33
- 36
- …

### Multiples of 4

A multiple of 4 is any number that can be divided by 4 without leaving a remainder. The first few multiples of 4 are:

- 4
- 8
- 12
- 16
- 20
- 24
- 28
- 32
- 36
- 40
- …

To identify multiple of 4. One way is to use the following divisibility rule:

**A number is divisible by 4 if the last two digits are divisible by 4.**

For example, the number 124 is a multiple of 4 because the last two digits, 24, are divisible by 4.

Another way to identify multiples of 4 is to use the following divisibility rule:

**A number is divisible by 4 if the sum of the digits is divisible by 4.**

For example, the number 124 is a multiple of 4 because the sum of the digits, 1 + 2 + 4 = 7, is divisible by 4.

### Multiples of 5

A multiple of 5 is any number that can be divided by 5 without a remainder. The first few multiples of 5 are:

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ...

There is no limit to the number of multiples of 5. Any number that can be expressed as a product of 5 and any other integer is a multiple of 5. For example, 140, 145, and 180 are all multiples of 5 because they can be divided by 5 without a remainder.

To determine if a number is a multiple of 5, you can simply look at the last digit. If the last digit is a 0 or a 5, then the number is a multiple of 5. For example, 50 and 125 are both multiples of 5 because the last digit is a 0.

### Multiples of 6

A multiple of 6 is any number that can be divided by 6 without a remainder.

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...

Any number that can be expressed in the form $6n$, where $n$ is any integer, is a multiple of 6. For example, 18 is a multiple of 6 because $18=6×3$.

Multiples of 6 can be even or odd. All even numbers are multiples of 6, because any even number can be expressed in the form $2n$, where $n$ is any integer, and 2 is a multiple of 6. However, not all odd numbers are multiples of 6. For example, 1 is not a multiple of 6, because it cannot be expressed in the form $6n$, where $n$ is any integer.

**Multiples** of **7**

7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, …

Any number that is a multiple of 7 can be written in the form 7n, where n is any natural number. For example, 21 is a multiple of 7 because 21 = 7 * 3.

You can also find multiples of 7 by looking for patterns. For example, all even numbers that end in a 4 are multiples of 7. All odd numbers that end in a 1 are multiples of 7.

### Multiples of 8

Multiples of 8 are numbers that can be divided by 8 without leaving a remainder. The first few multiples of 8 are:

8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, …

To find out if a number is a multiple of 8, you can divide it by 8. If the result is a whole number, then the number is a multiple of 8. For example, 16 divided by 8 is 2, so 16 is a multiple of 8.

### Multiples of 9

A multiple of 9 is any number that is divisible by 9 without leaving a remainder. The first ten multiples of 9 are:

9, 18, 27, 36, 45, 54, 63, 72, 81, and 90.

Here are some ways to identify multiples of 9:

**Look at the digits of the number.**If the sum of the digits is divisible by 9, then the number is also divisible by 9. For example, the sum of the digits in the number 54 is 9 (5 + 4), so 54 is a multiple of 9.**Divide the number by 9.**If the remainder is 0, then the number is divisible by 9. For example, 45 divided by 9 leaves a remainder of 0, so 45 is a multiple of 9.

### Multiples of 10

There are a few ways to identify multiples of 10. One way is to look at the last digit of the number. If the last digit is a 0, then the number is a multiple of 10. Another way to identify multiples of 10 is to divide the number by 10. If the remainder is 0, then the number is a multiple of 10.

### Multiples of 11

11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, ...

To find if a number is a multiple of 11, you can use the following steps:

- Add the digits in the even places of the number.
- Add the digits in the odd places of the number.
- Subtract the smaller sum from the larger sum.
- If the difference is divisible by 11, then the original number is also divisible by 11.

For example, the number 121 has a sum of digits of 4, which is divisible by 11, so 121 is a multiple of 11.

### Multiples of 12

The multiples of 12 are all the numbers that can be divided by 12 without a remainder.

12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, ...

To find the multiples of 12, you can simply multiply 12 by any positive integer. For example, to find the third multiple of 12, you would multiply 12 by 3. This gives you 36, which is the third multiple of 12.

### Multiples of 13

Multiples of 13 are numbers that can be divided by 13 without leaving a remainder.

13, 26, 39, 52, 65, 78, 91, 104, 117, 130

To find other multiples of 13, simply add 13 to any of the numbers in the list above. For example, 13 + 13 = 26, so 26 is also a multiple of 13. You can also multiply any of the numbers in the list above by 13 to get another multiple of 13. For example, 13 x 2 = 26, so 26 is also a multiple of 13.

### Multiples of 14

14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, …

To find multiples of 14, you can simply multiply 14 by any positive integer. For example, 14 × 2 = 28, 14 × 3 = 42, and so on.

Another way to find the multiples of a number is to look for patterns. For example, we can see that the multiples of 14 all have a 2 as the last digit. This means that any number with a 2 as the last digit is a multiple of 14.

We can also use prime factorization to find the multiples of a number. The prime factorization of 14 is 2 * 7. This means that any number that is a multiple of 2 and 7 is also a multiple of 14. For example, 28 is a multiple of 14 because it is a multiple of 2 and 7 (28 = 2 * 2 * 7).

### Multiples of 15

Multiples of 15 are numbers that can be divided by 15 without a remainder.

15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, ...

You can find any multiple of 15 by multiplying 15 by any integer. For example, 15 × 2 = 30, so 30 is a multiple of 15.

### Multiples of 16

Multiples of 16 are numbers that can be divided by 16 without leaving a remainder.

16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 256, 272, 288, 304, 320, 336, 352, 368, 384, 400, 416, …

To find more multiples of 16, you can simply multiply 16 by any natural number. For example, 16 x 1 = 16, 16 x 2 = 32, 16 x 3 = 48, and so on.

### Multiples of 17

The multiples of 17 are any number that is divisible by 17 without leaving a remainder. The first few multiples of 17 are:

17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 272, 289, 306, 323, 340, 357, 374, 391, 408, 425, 442, 459, 476, 493, 510, 527, 544, 561, 578, 595, 612, 629, 646, 663, 680, 697, 714, 731, 748, 765, 782, 799, 816, 833, 850, 867, 884, 901, 918, 935, 952, 969, 986

To find more multiples of 17, we can simply add 17 to any previous multiple.

### Multiples of 18

Multiples of 18 are numbers that are divisible by 18 without leaving a remainder.

18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252, 270, …

To find multiples of 18, you can simply multiply 18 by any positive integer. For example, 18 x 2 = 36, 18 x 3 = 54, and so on.

### Multiples of 19

Multiples of 19 are the numbers that are divisible by 19 without leaving a remainder.

19, 38, 57, 76, 95, 114, 133, 152, 171, 190, 209, 228, 247, 266, 285, 304, 323, 342, 361, 380, 399

To find more multiples of 19, you can simply add 19 to any of the numbers on the list above. For example, 209 + 19 = 228, so 228 is also a multiple of 19.

### Multiples of 20

The multiples of 20 are all the numbers that can be divided by 20 without leaving a remainder. The first few multiples of 20 are:

20, 40, 60, 80, 100, 120, 140, 160, 180, 200, ...

To determine if a number is a multiple of 20:

**Look at the last two digits.**If the last two digits of a number are divisible by 20, then the number is divisible by 20. For example, the number 120 is divisible by 20 because the last two digits, 20, are divisible by 20.**Divide the number by 20.**If the number can be divided by 20 without leaving a remainder, then the number is a multiple of 20. For example, the number 100 is a multiple of 20 because 100 ÷ 20 = 5.**Use the prime factorization of 20.**20 is a product of the prime numbers 2 and 5. Therefore, in order for a number to be a multiple of 20, it must have at least two factors of 2 and one factor of 5. For example, the number 100 is a multiple of 20 because it has two factors of 2 (2 × 2 = 4) and one factor of 5 (100 ÷ 5 = 20).

### Multiples of 21

A multiple of 21 is any number that can be divided by 21 without a remainder.

21, 42, 63, 84, 105, 126, 147, 168, 189, 210, ...

you can also use the following steps to determine if a number is a multiple of 21:

- Divide the number by 3.
- Divide the result by 7.
- If the result is an integer, then the number is a multiple of 21.

For example, to determine if the number 126 is a multiple of 21, we would do the following:

- Divide 126 by 3: 126 ÷ 3 = 42
- Divide 42 by 7: 42 ÷ 7 = 6
- The result of step 2 is an integer, so 126 is a multiple of 21.

Another way to determine if a number is a multiple of 21 is to add up the digits of the number. If the sum of the digits is divisible by 3, then the number is also divisible by 3 and therefore a multiple of 21. The number 126 is a multiple of 21 because 1 + 2 + 6 = 9, and 9 is divisible by 3.

### Multiples of 22

Multiples of 22 are numbers that are divisible by 22.

22, 44, 66, 88, 110, 132, 154, 176, 198, 220, ...

To find multiples of 22, you can simply multiply 22 by any integer. For example, 22 x 2 = 44, 22 x 3 = 66, and so on.

### Multiples of 25

Multiples of 25 are numbers that can be divided by 25 without a remainder.

25, 50, 75, 100, 125, and so on

To determine if a number is a multiple of 25, there are a few things you can do:

**Look at the last two digits of the number.**If the last two digits are 00, 25, 50, or 75, then the number is a multiple of 25.**Divide the number by 25.**If the number is divisible by 25 without leaving a remainder, then the number is a multiple of 25.

### Multiples of 30

Multiples of 30 are numbers that are divisible by 30 without a remainder. The first 10 multiples of 30 are:

30, 60, 90, 120, 150, 180, 210, 240, 270, 300

A multiple of 30 is any number that can be divided by 30 without a remainder. To determine if a number is a multiple of 30, you can use the following rules:

- The number must be even.
- The sum of the digits in the number must be divisible by 3.

**Examples:**

- The number 60 is a multiple of 30 because it is even and the sum of its digits (6 + 0 = 6) is divisible by 3.
- The number 90 is a multiple of 30 because it is even and the sum of its digits (9 + 0 = 9) is divisible by 3.
- The number 120 is a multiple of 30 because it is even and the sum of its digits (1 + 2 + 0 = 3) is divisible by 3.

### Multiples of 36

The multiples of 36 are all the numbers that can be divided by 36 without a remainder.

36, 72, 108, 144, 180, 216, 252, 288, 324, 360, ...

To determine if a number is a multiple of 36 is to look at its prime factorization. The prime factorization of 36 is 2^2 * 3^2. This means that 36 can be divided evenly by 2, 2, 3, and 3. Therefore, any number that can be divided evenly by 2, 2, 3, and 3 is also a multiple of 36.

### Multiples of 96

Multiples of 96 are numbers that are divisible by 96.

96, 192, 288, 384, 480, 576, 672, 768, 864, 960

You can find more multiples of 96 by adding 96 to each of these numbers. For example, the next multiple of 96 is 96 + 96 = 192.

To determine if a number is a multiple of 96, you can also look at the prime factorization of both numbers. The prime factorization of 96 is 2^5 * 3. If a number has the prime factors 2 and 3, and the exponents of 2 and 3 are at least 5 and 1, respectively, then the number is a multiple of 96.

## Multiple of a natural number worksheet

For each question, determine whether the given number is a multiple of the natural number provided.

Is 24 a multiple of 4?

**Answer:** Yes, 24 is a multiple of 4 because 24 = 4 × 6.

Is 15 a multiple of 3?

**Answer:** Yes, 15 is a multiple of 3 because 15 = 3 × 5.

Is 18 a multiple of 6?

**Answer:** Yes, 18 is a multiple of 6 because 18 = 6 × 3.

Is 50 a multiple of 7?

**Answer:** No, 50 is not a multiple of 7. There is no whole number that you can multiply by 7 to get 50.

Is 63 a multiple of 9?

**Answer:** Yes, 63 is a multiple of 9 because 63 = 9 × 7.

Is 28 a multiple of 2?

**Answer:** Yes, 28 is a multiple of 2 because 28 = 2 × 14.

Is 45 a multiple of 5?

**Answer:** Yes, 45 is a multiple of 5 because 45 = 5 × 9.

Is 72 a multiple of 12?

**Answer:** Yes, 72 is a multiple of 12 because 72 = 12 × 6.

Is 33 a multiple of 11?

**Answer:** Yes, 33 is a multiple of 11 because 33 = 11 × 3.

Is 20 a multiple of 15?

**Answer:** No, 20 is not a multiple of 15. There is no whole number that you can multiply by 15 to get 20.

Is 0 a multiple of any natural number?

**Answer:** Yes, 0 is a multiple of any natural number because 0 times any natural number is always 0.

Multiple of a natural number To Arithmetic course and exercises