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Table of Contents

Contents

Multiples are a fundamental concept in mathematics that has numerous practical applications. As we all know, multiplication tables serve as the foundation for finding the multiples of given numbers.

This article will explain what multiples are in mathematics, how to find the multiples of a given integer, and give detailed examples of multiples. Scroll down to find out more.

Looking to Learn Math? Explore Wiingy’s Online Math Tutoring Services to learn from top mathematicians and experts.

The properties of multiples are explained below.

A given integer has an unlimited number of multiples. As an illustration, let’s put M(2) = 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, etc. for the multiples of 2.

All numbers are multiples of one another. Example: 3=3×1, where 3 is a multiple of 3.

The result of multiplying any number by 0 is always 0. For instance, 0x2=0

A number is bigger than or equal to every multiple of that number. Multiples of 5 are known to be 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. Each multiple in this case is larger than or equal to 5.

The section below provides a step-by-step explanation of the multiples’ attributes.

**Example: **1 × 42 = 42

1 × 524 = 524

1 × 9 = 9

When we multiply 1 by any number, we obtain the provided number.

Example: 464 = 1 × 464

24 = 1 × 24

Given that we know that 1 is a factor, multiplying by 1 gives the same outcome.

Every number is therefore a multiple of it in and of itself.

Let’s write the multiples of 2 for illustration.

M(2) = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22,…..}

Since there are infinite numbers, there will also be an endless number of multiples of 2.

Thus, it demonstrates that “There are an unlimited number of multiples of a given integer.”

Every number has an indefinite number of multiples except for the number 0.

Example:

M(2) = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22,…..}

M(3) = {0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33,…}

M(…) = {…….}

Any number which multiplies with Zero will always result in 0.

Example: For instance, we obtain 0 when we multiply 2 by 0.

0 × 2 = 0

The result of multiplying 0 by 649 is 0.

0 × 649 = 0

The result of multiplying 25 by 0 is zero.

25 × 0 = 0

The result of multiplying 16 by 0 is zero.

The first 5 multiples of 2 to 100 are tabulated below:

Multiples of a Number | First 5 Multiples |

Multiples of 1 | 1, 2, 3, 4,5 |

Multiples of 2 | 2, 4, 6, 8, 10, 12 |

Multiples of 3 | 3, 6, 9, 12, 15, 18 |

Multiples of 4 | 4, 8, 12, 16, 20 |

Multiples of 5 | 5, 10, 15, 20, 25 |

Multiples of 6 | 6, 12, 18, 24, 30 |

Multiples of 7 | 7, 14, 21, 28, 35 |

Multiples of 8 | 8, 16, 24, 32, 40 |

Multiples of 9 | 9, 18, 27, 36, 45 |

Multiples of 10 | 10, 20, 30, 40, 50 |

Multiples of 11 | 11, 22, 33, 44, 55 |

Multiples of 12 | 12, 24, 36, 48, 60 |

Multiples of 13 | 13, 26, 39, 52, 65 |

Multiples of 14 | 14, 28, 42, 56, 70 |

Multiples of 15 | 15, 30, 45, 60, 75 |

Multiples of 16 | 16, 32, 48, 64, 80 |

Multiples of 17 | 17, 34, 51, 68, 85, 102 |

Multiples of 18 | 18, 36, 54, 72, 90 |

Multiples of 19 | 19, 38, 57, 76, 95 |

Multiples of 20 | 20, 40, 60, 80, 100 |

Multiples of 21 | 21, 42, 63, 84, 105 |

Multiples of 22 | 22, 44, 66, 88, 110 |

Multiples of 23 | 23, 46, 69, 92, 115 |

Multiples of 24 | 24, 48, 72, 96, 120 |

Multiples of 25 | 25, 50, 75, 100, 125 |

Multiples of 26 | 26, 52, 78, 104, 130 |

Multiples of 27 | 27, 54, 81, 108, 135 |

Multiples of 28 | 28, 56, 84, 112, 140 |

Multiples of 29 | 29, 58, 87, 116, 145 |

Multiples of 30 | 30, 60, 90, 120, 150 |

Multiples of 31 | 31, 62, 93, 124, 155 |

Multiples of 32 | 32, 64, 96, 128, 160 |

Multiples of 33 | 33, 66, 99, 132, 165 |

Multiples of 34 | 34 , 68 , 102 , 136 , 170 |

Multiples of 35 | 35 , 70 , 105 , 140 , 175 |

Multiples of 36 | 36 , 72 , 108 , 144 , 180 |

Multiples of 37 | 37 , 74 , 111 , 148 , 185 |

Multiples of 38 | 38 , 76 , 114 , 152 , 190 |

Multiples of 39 | 39 , 78 , 117 , 156 , 195 |

Multiples of 40 | 40 , 80 , 120 , 160 , 200 |

Multiples of 41 | 41 , 82 , 123 , 164 , 205 |

Multiples of 42 | 42 , 84 , 126 , 168 , 210 |

Multiples of 43 | 43 , 86 , 129 , 172 , 215 |

Multiples of 44 | 44 , 88 , 132 , 176 , 220 |

Multiples of 45 | 45 , 90 , 135 , 180 , 225 |

Multiples of 46 | 46 , 92 , 138 , 184 , 230 |

Multiples of 47 | 47 , 94 , 141 , 188 , 235 |

Multiples of 48 | 48 , 96 , 144 , 192 , 240 |

Multiples of 49 | 49 , 98 , 147 , 196 , 245 |

Multiples of 50 | 50 , 100 , 150 , 200 , 250 |

Multiples of 51 | 51 , 102 , 153 , 204 , 255 |

Multiples of 52 | 52 , 104 , 156 , 208 , 260 |

Multiples of 53 | 53 , 106 , 159 , 212 , 265 |

Multiples of 54 | 54 , 108 , 162 , 216 , 270 |

Multiples of 55 | 55 , 110 , 165 , 220 , 275 |

Multiples of 56 | 56 , 112 , 168 , 224 , 280 |

Multiples of 57 | 57 , 114 , 171 , 228 , 285 |

Multiples of 58 | 58 , 116 , 174 , 232 , 290 |

Multiples of 59 | 59 , 118 , 177 , 236 , 295 |

Multiples of 60 | 60 , 120 , 180 , 240 , 300 |

Multiples of 61 | 61 , 122 , 183 , 244 , 305 |

Multiples of 62 | 62 , 124 , 186 , 248 , 310 |

Multiples of 63 | 63 , 126 , 189 , 252 , 315 |

Multiples of 64 | 64 , 128 , 192 , 256 , 320 |

Multiples of 65 | 65 , 130 , 195 , 260 , 325 |

Multiples of 66 | 66 , 132 , 198 , 264 , 330 |

Multiples of 67 | 67 , 134 , 201 , 268 , 335 |

Multiples of 68 | 68 , 136 , 204 , 272 , 340 |

Multiples of 69 | 69 , 138 , 207 , 276 , 345 |

Multiples of 70 | 70 , 140 , 210 , 280 , 350 |

Multiples of 71 | 71 , 142 , 213 , 284 , 355 |

Multiples of 72 | 72 , 144 , 216 , 288 , 360 |

Multiples of 73 | 73 , 146 , 219 , 292 , 365 |

Multiples of 74 | 74 , 148 , 222 , 296 , 370 |

Multiples of 75 | 75 , 150 , 225 , 300 , 375 |

Multiples of 76 | 76 , 152 , 228 , 304 , 380 |

Multiples of 77 | 77 , 154 , 231 , 308 , 385 |

Multiples of 78 | 78 , 156 , 234 , 312 , 390 |

Multiples of 79 | 79 , 158 , 237 , 316 , 395 |

Multiples of 80 | 80 , 160 , 240 , 320 , 400 |

Multiples of 81 | 81 , 162 , 243 , 324 , 405 |

Multiples of 82 | 82 , 164 , 246 , 328 , 410 |

Multiples of 83 | 83 , 166 , 249 , 332 , 415 |

Multiples of 84 | 84 , 168 , 252 , 336 , 420 |

Multiples of 85 | 85 , 170 , 255 , 340 , 425 |

Multiples of 86 | 86 , 172 , 258 , 344 , 430 |

Multiples of 87 | 87 , 174 , 261 , 348 , 435 |

Multiples of 88 | 88 , 176 , 264 , 352 , 440 |

Multiples of 89 | 89 , 178 , 267 , 356 , 445 |

Multiples of 90 | 90 , 180 , 270 , 360 , 450 |

Multiples of 91 | 91 , 182 , 273 , 364 , 455 |

Multiples of 92 | 92 , 184 , 276 , 368 , 460 |

Multiples of 93 | 93 , 186 , 279 , 372 , 465 |

Multiples of 94 | 94 , 188 , 282 , 376 , 470 |

Multiples of 95 | 95 , 190 , 285 , 380 , 475 |

Multiples of 96 | 96 , 192 , 288 , 384 , 480 |

Multiples of 97 | 97 , 194 , 291 , 388 , 485 |

Multiples of 98 | 98 , 196 , 294 , 392 , 490 |

Multiples of 99 | 99 , 198 , 297 , 396 , 495 |

Multiples of 100 | 100, 200, 300, 400, 500 |

The multiples that a certain group of numbers share are known as common multiples.

For example, we can list the multiples of 3 and 6 individually and then look for the multiples that appear in both lists to determine the common multiples of 3 and 6, for instance.

You can list the multiples of three as 3, 6, 9, 12, 15, and so on. You can list the multiples of six as 6, 12, 18, 24, 30, 36, and so on.

The multiples that are present in both lists, assuming we discover them, are 6, 12, and 18. The term “common multiples of 3 and 6” refers to these.

**Common Multiples of 6 and 8**

Multiples of 6 = 6,12,18,**24**,30,36,42,**48**

Multiples of 8 = 8,16,**24**,32,40,**48**,56

Thus, the common multiples of 6 and 8 can be listed as, 24, 48, and so on.

**Definition of Factors: **Factors are those numbers that divide another number exactly while leaving a zero as the remainder. Another way to put it is that the factor of the dividend is the divisor if the dividend is exactly divided by the factor, leaving zero factors. Every number shares the number itself and the number one in common.

Both factors and multiples are related to each other. For example, the number 20 is a multiple of the digits 4 and 5. Alternatively, the factors of the number 20 are the digits 4 and 5.

Here, factors have divided the other number without any remainder. Similarly, when one number is multiplied by another, we have got the products that are known as multiples.

Finding all the finite integers that divide the given number so that there is no remainder after division is necessary to determine a number’s factors.

For example, if we use the number 28, as an example, then 28, 14, 7, 4, 2, and 1 are all the integers that divide 28 perfectly. Therefore, each of these numbers is a factor of the number 28. The number itself and the number 1 are the two fundamental components of every number, it should be remembered.

The difference between factors and multiples are given below:

Factor | Multiples |

1. The exact divisors of a number are referred to as factors. | 1. The result of multiplying two or more integers is known as a multiple. |

2. Division is the procedure used to identify a number’s factors. | 2. Multiplication is the procedure used to find the multiples. |

3. The result of the variables must be less than or equal to the specified amount. | 3. The results of the multiples must exceed or be equal to the specified number. |

4. There are a finite number of components. | 4. There are an unlimited amount of multiples. |

You should look through examples of different types of factors and multiples in order to comprehend the notion of factors and multiples. Additionally, a few specific qualities help to make the idea obvious and succinct. The following list of important properties includes some:

There is one thing that all numbers have in common: 1

There is a multiple of every number, namely 0.

Only whole numbers can use the multiples and factors concepts.

Every number consists of at least two components, namely the number 1 and the actual number.

The largest element is the number itself, and the smallest factor is the number 1.

The number itself is the only multiple of each number. There is a finite number of factors and an infinite number of multiples of each number.

If a number only contains the number itself and the number 1, it is said to be a prime number.

A few solved examples of Multiples are explained below:

**Solved Example 1: What are the first 3 multiples of 11?Answer:** The first 3 multiples of 11 in the set of Natural Numbers are: 0, 11, 22

11 is a multiple of 11 because 11 x 1 = 11

22 is a multiple of 11 because 11 x 2 = 22

**Solved Example 2: What are 5 multiples of 17?Answer: **The first five multiples of 17 are 17, 34, 51, 68, 85, 102, etc.

We can observe that it is a sequence where the difference between each next number and the preceding number, i.e., two consecutive multiples or products, is equal to 17.

**Solved Example 3: What is the smallest multiple of 17?**The smallest multiple of 17 is 0. Apart from zero, 17 is the smallest multiple of 17.

**Solved Example 4: What can we multiply to get 17?Answer:** To get 17, we need to multiply 17 with 1 or 1 with 17.

17 x 1 = 17

1 x 17 = 17

**Solved Example 5: What is 60 a multiple of?**60 is a multiple of 6. Thus, 6 and all its multiples are common multiples of 6 and 60.

**Solved Example 6: 10, 30, 50, 60 are all the multiples of ___Answer: **10, 30, 50, and 60 are multiples of 1, 2, 5, and 10.

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**What are multiples in math?**

In mathematics, multiples are the results of multiplying an integer by a given number. For example, Multiples of 5 include, 10, 15, 20, 25, 30, etc. Whereas Multiples of 7 include 14, 21, 28, 35, 42, 49, etc.

**What do we mean by multiples?**

Multiples are the results of multiplying an integer by a given number in mathematics.

**What are the multiples of 12?**

Multiples of 12 are 24, 36, 48, 60, 72, 84, 96, 120, and so on. It is a series where there are two successive multiples or products and there is a 12 difference between each number after the previous number.

**What is a multiple of 3?**

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.

**What are all multiples of 6?**

The multiples of six are 6, 12, 18, 24, 30, 36, 42, 48, 54, and so on. It is a series where there are two successive multiples or products, with a difference of 6, between each number and the one before it.

**What are the multiples of 8?**

8, 16, 24, 32, 40, 48, 56, 64, 72, and so on are the multiples of 8 that can be found. It is a series when there are two consecutive results and there is an 8-digit difference between each subsequent number and the one before it. The numbers known as multiples are those that produce products when any number is multiplied by other natural numbers.

**How do you explain multiples to a child?**

In mathematics, multiples are the results of multiplying an integer by a given number. Kids can be taught that a multiple is a number that can be divided by another number without leaving a remainder a certain number of times.

**How many multiples does a number have?**

A number has an unlimited number of multiples.

The multiples of a number are therefore unlimited. To list the multiples of 3, for instance, we would begin with 3, 6, 9, 12, 15, 18, and so on.

**How do you determine multiples?**

Multiply the integer by any whole number to discover its multiples. For example, 15 is the third multiple of 5 since 5 X 3 = 15.

**What is a multiple of 10?**

10, 20, 30, 40, 50, 60, 70, 80, 90, and 100 are the multiples of 10.

Practice Quiz

Questions: 1/2

Wrong Answer

Each charity would receive 30.2 dollars (151 divided by 5 = 30.2).