## Multiples of 14

Multiples of 14 are numbers obtained by multiplying 14 with integers. In mathematics, these numbers are integral parts of the number system. Each multiple is a product of 14 and another integer, illustrating the concept of multiplication. Multiples of 14 can also be seen as having 14 as one of their divisors or factors. Understanding multiples helps in grasping broader mathematical concepts such as divisibility and common factors.

## What are Multiples of 14?

Multiples of 14 are numbers that can be expressed as 14 times an integer. In other words, any number that results from multiplying 14 by any whole number is a multiple of 14. Examples include 14, 28, 42, 56, and so on.

**Prime Factorization of 14:**14 = 2 × 7

**First 10 multiples of 14:**14, 28, 42, 56, 70, 84, 98, 112, 126, 140.

## For example, 28, 56, 98 and 126 are all multiples of 14, 175 is not a multiple of 14 for the following reasons:

Number | Division by 14 | Remainder |
---|---|---|

28 | 28 ÷ 14 = 2 | 0 |

56 | 56 ÷ 14 = 4 | 0 |

98 | 98 ÷ 14 = 7 | 0 |

126 | 126 ÷ 14 = 9 | 0 |

175 | 175 ÷ 14 = 12 is not an exact multiple of 14. | 7 |

## Read More About Multiples of 14

## List of First 100 Multiples of 14 with Remainders

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

14 | 14÷14 = 1, so 14 is divisible by 14. | 0 |

28 | 28÷14 = 2, so 28 is divisible by 14. | 0 |

42 | 42÷14 = 3, so 42 is divisible by 14. | 0 |

56 | 56÷14 = 4, so 56 is divisible by 14. | 0 |

70 | 70÷14 = 5, so 70 is divisible by 14. | 0 |

84 | 84÷14 = 6, so 84 is divisible by 14. | 0 |

98 | 98÷14 = 7, so 98 is divisible by 14. | 0 |

112 | 112÷14 = 8, so 112 is divisible by 14. | 0 |

126 | 126÷14 = 9, so 126 is divisible by 14. | 0 |

140 | 140÷14 = 10, so 140 is divisible by 14. | 0 |

154 | 154÷14 = 11, so 154 is divisible by 14. | 0 |

168 | 168÷14 = 12, so 168 is divisible by 14. | 0 |

182 | 182÷14 = 13, so 182 is divisible by 14. | 0 |

196 | 196÷14 = 14, so 196 is divisible by 14. | 0 |

210 | 210÷14 = 15, so 210 is divisible by 14. | 0 |

224 | 224÷14 = 16, so 224 is divisible by 14. | 0 |

238 | 238÷14 = 17, so 238 is divisible by 14. | 0 |

252 | 252÷14 = 18, so 252 is divisible by 14. | 0 |

266 | 266÷14 = 19, so 266 is divisible by 14. | 0 |

280 | 280÷14 = 20, so 280 is divisible by 14. | 0 |

294 | 294÷14 = 21, so 294 is divisible by 14. | 0 |

308 | 308÷14 = 22, so 308 is divisible by 14. | 0 |

322 | 322÷14 = 23, so 322 is divisible by 14. | 0 |

336 | 336÷14 = 24, so 336 is divisible by 14. | 0 |

350 | 350÷14 = 25, so 350 is divisible by 14. | 0 |

364 | 364÷14 = 26, so 364 is divisible by 14. | 0 |

378 | 378÷14 = 27, so 378 is divisible by 14. | 0 |

392 | 392÷14 = 28, so 392 is divisible by 14. | 0 |

406 | 406÷14 = 29, so 406 is divisible by 14. | 0 |

420 | 420÷14 = 30, so 420 is divisible by 14. | 0 |

434 | 434÷14 = 31, so 434 is divisible by 14. | 0 |

448 | 448÷14 = 32, so 448 is divisible by 14. | 0 |

462 | 462÷14 = 33, so 462 is divisible by 14. | 0 |

476 | 476÷14 = 34, so 476 is divisible by 14. | 0 |

490 | 490÷14 = 35, so 490 is divisible by 14. | 0 |

504 | 504÷14 = 36, so 504 is divisible by 14. | 0 |

518 | 518÷14 = 37, so 518 is divisible by 14. | 0 |

532 | 532÷14 = 38, so 532 is divisible by 14. | 0 |

546 | 546÷14 = 39, so 546 is divisible by 14. | 0 |

560 | 560÷14 = 40, so 560 is divisible by 14. | 0 |

574 | 574÷14 = 41, so 574 is divisible by 14. | 0 |

588 | 588÷14 = 42, so 588 is divisible by 14. | 0 |

602 | 602÷14 = 43, so 602 is divisible by 14. | 0 |

616 | 616÷14 = 44, so 616 is divisible by 14. | 0 |

630 | 630÷14 = 45, so 630 is divisible by 14. | 0 |

644 | 644÷14 = 46, so 644 is divisible by 14. | 0 |

658 | 658÷14 = 47, so 658 is divisible by 14. | 0 |

672 | 672÷14 = 48, so 672 is divisible by 14. | 0 |

686 | 686÷14 = 49, so 686 is divisible by 14. | 0 |

700 | 700÷14 = 50, so 700 is divisible by 14. | 0 |

714 | 714÷14 = 51, so 714 is divisible by 14. | 0 |

728 | 728÷14 = 52, so 728 is divisible by 14. | 0 |

742 | 742÷14 = 53, so 742 is divisible by 14. | 0 |

756 | 756÷14 = 54, so 756 is divisible by 14. | 0 |

770 | 770÷14 = 55, so 770 is divisible by 14. | 0 |

784 | 784÷14 = 56, so 784 is divisible by 14. | 0 |

798 | 798÷14 = 57, so 798 is divisible by 14. | 0 |

812 | 812÷14 = 58, so 812 is divisible by 14. | 0 |

826 | 826÷14 = 59, so 826 is divisible by 14. | 0 |

840 | 840÷14 = 60, so 840 is divisible by 14. | 0 |

854 | 854÷14 = 61, so 854 is divisible by 14. | 0 |

868 | 868÷14 = 62, so 868 is divisible by 14. | 0 |

882 | 882÷14 = 63, so 882 is divisible by 14. | 0 |

896 | 896÷14 = 64, so 896 is divisible by 14. | 0 |

910 | 910÷14 = 65, so 910 is divisible by 14. | 0 |

924 | 924÷14 = 66, so 924 is divisible by 14. | 0 |

938 | 938÷14 = 67, so 938 is divisible by 14. | 0 |

952 | 952÷14 = 68, so 952 is divisible by 14. | 0 |

966 | 966÷14 = 69, so 966 is divisible by 14. | 0 |

980 | 980÷14 = 70, so 980 is divisible by 14. | 0 |

994 | 994÷14 = 71, so 994 is divisible by 14. | 0 |

1008 | 1008÷14 = 72, so 1008 is divisible by 14. | 0 |

1022 | 1022÷14 = 73, so 1022 is divisible by 14. | 0 |

1036 | 1036÷14 = 74, so 1036 is divisible by 14. | 0 |

1050 | 1050÷14 = 75, so 1050 is divisible by 14. | 0 |

1064 | 1064÷14 = 76, so 1064 is divisible by 14. | 0 |

1078 | 1078÷14 = 77, so 1078 is divisible by 14. | 0 |

1092 | 1092÷14 = 78, so 1092 is divisible by 14. | 0 |

1106 | 1106÷14 = 79, so 1106 is divisible by 14. | 0 |

1120 | 1120÷14 = 80, so 1120 is divisible by 14. | 0 |

1134 | 1134÷14 = 81, so 1134 is divisible by 14. | 0 |

1148 | 1148÷14 = 82, so 1148 is divisible by 14. | 0 |

1162 | 1162÷14 = 83, so 1162 is divisible by 14. | 0 |

1176 | 1176÷14 = 84, so 1176 is divisible by 14. | 0 |

1190 | 1190÷14 = 85, so 1190 is divisible by 14. | 0 |

1204 | 1204÷14 = 86, so 1204 is divisible by 14. | 0 |

1218 | 1218÷14 = 87, so 1218 is divisible by 14. | 0 |

1232 | 1232÷14 = 88, so 1232 is divisible by 14. | 0 |

1246 | 1246÷14 = 89, so 1246 is divisible by 14. | 0 |

1260 | 1260÷14 = 90, so 1260 is divisible by 14. | 0 |

1274 | 1274÷14 = 91, so 1274 is divisible by 14. | 0 |

1288 | 1288÷14 = 92, so 1288 is divisible by 14. | 0 |

1302 | 1302÷14 = 93, so 1302 is divisible by 14. | 0 |

1316 | 1316÷14 = 94, so 1316 is divisible by 14. | 0 |

1330 | 1330÷14 = 95, so 1330 is divisible by 14. | 0 |

1344 | 1344÷14 = 96, so 1344 is divisible by 14. | 0 |

1358 | 1358÷14 = 97, so 1358 is divisible by 14. | 0 |

1372 | 1372÷14 = 98, so 1372 is divisible by 14. | 0 |

1386 | 1386÷14 = 99, so 1386 is divisible by 14. | 0 |

1400 | 1400÷14 = 100, so 1400 is divisible by 14. | 0 |

## Important Notes

**Exact Division**:

- A number is a multiple of 14 if it can be divided by 14 without any remainder.

**Zero Remainder**:

- When dividing a number by 14, if the remainder is 0, the number is a multiple of 14.

**Examples of Multiples**:

**28**: 28÷14 = 2, remainder 0.**56**: 56÷14 = 4, remainder 0.**98**: 98÷14 = 7, remainder 0.**126**: 126÷14 = 9, remainder 0.

**Non-Multiples**:

- If the division of a number by 14 results in a remainder other than 0, the number is not a multiple of 14.
- Example:
**175**: 175÷14 = 12 remainder 7.

**Verification**:

- To verify if a number is a multiple of 14, divide the number by 14 and check if the remainder is 0. If yes, it’s a multiple; if not, it’s not a multiple.

## Examples on Multiples of 14

### Basic Examples

### Example 1: 14

- Calculation: 14÷14 = 1
- Remainder: 0
**Explanation**: 14 is the first multiple of 14.

### Example 2: 28

- Calculation: 28÷14=2
- Remainder: 0
**Explanation**: 28 is the second multiple of 14.

### Example 3: 42

- Calculation: 42÷14 = 3
- Remainder: 0
**Explanation**: 42 is the third multiple of 14.

### Intermediate Examples

### Example 4: 56

- Calculation: 56÷14 = 4
- Remainder: 0
**Explanation**: 56 is the fourth multiple of 14.

### Example 5: 70

- Calculation: 70÷14 = 5
- Remainder: 0
**Explanation**: 70 is the fifth multiple of 14.

### Example 6: 84

- Calculation: 84÷14 = 6
- Remainder: 0
**Explanation**: 84 is the sixth multiple of 14.

#### Advanced Examples

### Example 7: 98

- Calculation: 98÷14 = 7
- Remainder: 0
**Explanation**: 98 is the seventh multiple of 14.

### Example 8: 112

- Calculation: 112÷14 = 8
- Remainder: 0
**Explanation**: 112 is the eighth multiple of 14.

### Example 9: 126

- Calculation: 126÷14 = 9
- Remainder: 0
**Explanation**: 126 is the ninth multiple of 14.

#### Higher Examples

### Example 10: 140

- Calculation: 140÷14 = 10
- Remainder: 0
**Explanation**: 140 is the tenth multiple of 14.

### Example 11: 154

- Calculation: 154÷14 = 11
- Remainder: 0
**Explanation**: 154 is the eleventh multiple of 14.

### Example 12: 168

- Calculation: 168÷14 = 12
- Remainder: 0
**Explanation**: 168 is the twelfth multiple of 14.

## FAQs

## What is a multiple of 14?

A multiple of 14 is a number that can be divided by 14 without leaving a remainder. For example, 28, 56, and 98 are all multiples of 14.

## How can you determine if a number is a multiple of 14?

To determine if a number is a multiple of 14, divide the number by 14. If the division results in an integer with no remainder, then the number is a multiple of 14.

## What are the first five multiples of 14?

The first five multiples of 14 are 14, 28, 42, 56, and 70.

## Is 84 a multiple of 14?

Yes, 84 is a multiple of 14 because 84÷14 = 6 with no remainder.

## Why is 175 not a multiple of 14?

175 is not a multiple of 14 because when divided by 14, it leaves a remainder. 175÷14 = 12 with a remainder of 7.

## Can a negative number be a multiple of 14?

Yes, negative numbers can be multiples of 14. For example, -14, -28, and -42 are all multiples of 14.

## What is the 10th multiple of 14?

The 10th multiple of 14 is 140, because 14×10 = 140.

## Are all multiples of 14 also multiples of 7?

Yes, all multiples of 14 are also multiples of 7 because 14 itself is a multiple of 7.

## How are multiples of 14 useful in real life?

Multiples of 14 can be useful in various real-life scenarios such as scheduling events every 14 days, calculating weekly salaries over multiple weeks, and organizing items into groups of 14.

## What is the difference between a factor and a multiple of 14?

A factor of 14 is a number that divides 14 without leaving a remainder, such as 1, 2, 7, and 14. A multiple of 14 is a number that can be expressed as 14 times an integer, such as 14, 28, 42, and so on.