## Multiples of 7

Multiples of 7 are numbers obtained by multiplying 7 by any integer. In mathematics, these numbers, such as 7, 14, 21, and 28, are the product of 7 and another whole number. Understanding multiples involves recognizing factors and divisors, as a multiple of 7 can be evenly divided by 7 without leaving a remainder. Identifying multiples of 7 is crucial in various mathematical applications, including finding common multiples and solving divisibility problems.

## What are Multiples of 7?

**Multiples of 7 are numbers that result from multiplying 7 by any integer.** They include 7, 14, 21, 28, and so on, where each number is a product of 7 and a whole number. These numbers can be evenly divided by 7 without leaving a remainder.

**Prime Factorization of 7:**1 × 7

**First five multiples of 7:**7, 14, 21, 28, 35, 42, 48, 56, 63, 70.

## For example, 21, 35, 63,70 are all multiples of 7, 73 is not a multiple of 7 for the following reasons:

Number | Calculation | Remainder |
---|---|---|

21 | 21 ÷ 7 = 3 | 0 |

35 | 35 ÷ 7 = 5 | 0 |

63 | 63 ÷ 7 = 9 | 0 |

70 | 70 ÷ 7 = 10 | 0 |

73 | 73 ÷ 7 = 10.4286 | 3 |

## List of First 100 Multiples of 7 with Remainders

Number | Calculation | Remainder |
---|---|---|

7 | 7 ÷ 7 = 1 | 0 |

14 | 14 ÷ 7 = 2 | 0 |

21 | 21 ÷ 7 = 3 | 0 |

28 | 28 ÷ 7 = 4 | 0 |

35 | 35 ÷ 7 = 5 | 0 |

42 | 42 ÷ 7 = 6 | 0 |

49 | 49 ÷ 7 = 7 | 0 |

56 | 56 ÷ 7 = 8 | 0 |

63 | 63 ÷ 7 = 9 | 0 |

70 | 70 ÷ 7 = 10 | 0 |

77 | 77 ÷ 7 = 11 | 0 |

84 | 84 ÷ 7 = 12 | 0 |

91 | 91 ÷ 7 = 13 | 0 |

98 | 98 ÷ 7 = 14 | 0 |

105 | 105 ÷ 7 = 15 | 0 |

112 | 112 ÷ 7 = 16 | 0 |

119 | 119 ÷ 7 = 17 | 0 |

126 | 126 ÷ 7 = 18 | 0 |

133 | 133 ÷ 7 = 19 | 0 |

140 | 140 ÷ 7 = 20 | 0 |

147 | 147 ÷ 7 = 21 | 0 |

154 | 154 ÷ 7 = 22 | 0 |

161 | 161 ÷ 7 = 23 | 0 |

168 | 168 ÷ 7 = 24 | 0 |

175 | 175 ÷ 7 = 25 | 0 |

182 | 182 ÷ 7 = 26 | 0 |

189 | 189 ÷ 7 = 27 | 0 |

196 | 196 ÷ 7 = 28 | 0 |

203 | 203 ÷ 7 = 29 | 0 |

210 | 210 ÷ 7 = 30 | 0 |

217 | 217 ÷ 7 = 31 | 0 |

224 | 224 ÷ 7 = 32 | 0 |

231 | 231 ÷ 7 = 33 | 0 |

238 | 238 ÷ 7 = 34 | 0 |

245 | 245 ÷ 7 = 35 | 0 |

252 | 252 ÷ 7 = 36 | 0 |

259 | 259 ÷ 7 = 37 | 0 |

266 | 266 ÷ 7 = 38 | 0 |

273 | 273 ÷ 7 = 39 | 0 |

280 | 280 ÷ 7 = 40 | 0 |

287 | 287 ÷ 7 = 41 | 0 |

294 | 294 ÷ 7 = 42 | 0 |

301 | 301 ÷ 7 = 43 | 0 |

308 | 308 ÷ 7 = 44 | 0 |

315 | 315 ÷ 7 = 45 | 0 |

322 | 322 ÷ 7 = 46 | 0 |

329 | 329 ÷ 7 = 47 | 0 |

336 | 336 ÷ 7 = 48 | 0 |

343 | 343 ÷ 7 = 49 | 0 |

350 | 350 ÷ 7 = 50 | 0 |

357 | 357 ÷ 7 = 51 | 0 |

364 | 364 ÷ 7 = 52 | 0 |

371 | 371 ÷ 7 = 53 | 0 |

378 | 378 ÷ 7 = 54 | 0 |

385 | 385 ÷ 7 = 55 | 0 |

392 | 392 ÷ 7 = 56 | 0 |

399 | 399 ÷ 7 = 57 | 0 |

406 | 406 ÷ 7 = 58 | 0 |

413 | 413 ÷ 7 = 59 | 0 |

420 | 420 ÷ 7 = 60 | 0 |

427 | 427 ÷ 7 = 61 | 0 |

434 | 434 ÷ 7 = 62 | 0 |

441 | 441 ÷ 7 = 63 | 0 |

448 | 448 ÷ 7 = 64 | 0 |

455 | 455 ÷ 7 = 65 | 0 |

462 | 462 ÷ 7 = 66 | 0 |

469 | 469 ÷ 7 = 67 | 0 |

476 | 476 ÷ 7 = 68 | 0 |

483 | 483 ÷ 7 = 69 | 0 |

490 | 490 ÷ 7 = 70 | 0 |

497 | 497 ÷ 7 = 71 | 0 |

504 | 504 ÷ 7 = 72 | 0 |

511 | 511 ÷ 7 = 73 | 0 |

518 | 518 ÷ 7 = 74 | 0 |

525 | 525 ÷ 7 = 75 | 0 |

532 | 532 ÷ 7 = 76 | 0 |

539 | 539 ÷ 7 = 77 | 0 |

546 | 546 ÷ 7 = 78 | 0 |

553 | 553 ÷ 7 = 79 | 0 |

560 | 560 ÷ 7 = 80 | 0 |

567 | 567 ÷ 7 = 81 | 0 |

574 | 574 ÷ 7 = 82 | 0 |

581 | 581 ÷ 7 = 83 | 0 |

588 | 588 ÷ 7 = 84 | 0 |

595 | 595 ÷ 7 = 85 | 0 |

602 | 602 ÷ 7 = 86 | 0 |

609 | 609 ÷ 7 = 87 | 0 |

616 | 616 ÷ 7 = 88 | 0 |

623 | 623 ÷ 7 = 89 | 0 |

630 | 630 ÷ 7 = 90 | 0 |

637 | 637 ÷ 7 = 91 | 0 |

644 | 644 ÷ 7 = 92 | 0 |

651 | 651 ÷ 7 = 93 | 0 |

658 | 658 ÷ 7 = 94 | 0 |

665 | 665 ÷ 7 = 95 | 0 |

672 | 672 ÷ 7 = 96 | 0 |

679 | 679 ÷ 7 = 97 | 0 |

686 | 686 ÷ 7 = 98 | 0 |

693 | 693 ÷ 7 = 99 | 0 |

700 | 700 ÷ 7 = 100 | 0 |

## Read More About Multiples of 7

## Examples on Multiples of 7

### Example 1: Sharing Slices of Pizza

You have 21 slices of pizza and want to share them equally among 3 friends. Each friend gets: 21÷3 = 7 Since 21 can be divided evenly by 7, 21 is a multiple of 7.

### Example 2: Counting Weeks

If you count in weeks, every 7 days is a new week. For instance, after 5 weeks, you have: 7×5 = 35 So, 35 days is a multiple of 7, representing 5 weeks.

### Example 3: Packaging Items

You have 63 apples to pack into boxes, with each box holding 7 apples. The number of boxes needed will be: 63÷7 = 9 Since 63 can be divided evenly by 7, 63 is a multiple of 7, requiring 9 boxes.

## Practical Examples of Multiples of 7

### Example 1: Weekly Planning

If you plan a weekly schedule, every 7 days marks a new week. For instance, if today is Monday, the next Monday will be in: 7×1 = 7 days And two weeks later will be: 7×2 = 14 days This helps in organizing tasks and events on a weekly basis.

### Example 2: Classroom Arrangement

A teacher has 28 students and wants to arrange them into rows with 7 students per row. The number of rows needed is: 28÷7 = 4 Thus, 28 students can be evenly divided into 4 rows, showing that 28 is a multiple of 7.

### Example 3: Purchasing Supplies

A store sells notebooks in packs of 7. If you need 49 notebooks for a school project, you will buy: 49÷7 = 7 This means you need 7 packs of notebooks, as 49 is a multiple of 7.

### Example 4: Budgeting and Savings

If you save $7 every week, after 10 weeks you will have: 7×10 = 70 This shows how consistent savings in multiples of 7 can help in budgeting and reaching financial goals.

### Example 5: Athletic Training

In training sessions, a coach might schedule exercises in sets of 7. For instance, if an athlete completes 4 sets of 7 push-ups, the total number of push-ups is: 7×4 = 28This illustrates how multiples of 7 can be used to structure workouts effectively.

### Example 6: Party Planning

If you are planning a party and want to create gift bags, with each bag containing 7 items, and you have 56 items in total, you can make: 56÷7 = 8 This means you can create 8 gift bags, showing that 56 is a multiple of 7.

## FAQs

## What is a multiple of 7?

A multiple of 7 is any number that can be obtained by multiplying 7 by an integer. Examples include 7, 14, 21, and so on.

## How do you determine if a number is a multiple of 7?

To determine if a number is a multiple of 7, divide the number by 7. If the result is a whole number with no remainder, then it is a multiple of 7.

## What are the first five multiples of 7?

The first five multiples of 7 are 7, 14, 21, 28, and 35.

## Can negative numbers be multiples of 7?

Yes, negative numbers can also be multiples of 7. Examples include -7, -14, -21, and so on.

## What is the smallest multiple of 7?

The smallest positive multiple of 7 is 7 itself. The smallest negative multiple of 7 is -7.

## Is zero a multiple of 7?

Yes, zero is considered a multiple of 7 because 0÷7=0 with no remainder.

## How are multiples of 7 used in real life?

Multiples of 7 are used in various practical scenarios such as planning weekly schedules, budgeting, organizing events, and distributing items evenly.

## Can a number be a multiple of 7 and another number?

Yes, a number can be a multiple of 7 and another number. For example, 28 is a multiple of both 7 and 4.

## What is the difference between multiples of 7 and factors of 7?

Multiples of 7 are numbers obtained by multiplying 7 by integers (e.g., 14, 21), while factors of 7 are numbers that divide 7 evenly (e.g., 1 and 7).

## How can multiples of 7 be identified in a sequence of numbers?

To identify multiples of 7 in a sequence, check each number to see if it can be divided by 7 without leaving a remainder. Alternatively, look for patterns that match the multiplication table of 7.