## Multiples of 24

Multiples of 24 are the numbers that result from multiplying 24 by integers. In mathematics, these numbers can be expressed as 24, 48, 72, and so on, showcasing the results of multiplication. Each multiple of 24 can be divided evenly by 24, making 24 a common divisor among them. These multiples also represent a series of numbers where 24 is a factor. Understanding multiples of 24 helps in grasping concepts related to divisors, factors, and the broader number system in mathematics.

## What are Multiples of 24?

**Multiples of 24 are the numbers that can be expressed as 24n, where n is an integer.** These numbers are the result of multiplying 24 by whole numbers, starting from 0. Examples include 24, 48, 72, and so on.

**Prime factorization of 24**: 24 = 2 × 2 × 2 × 3

**First 10 multiples of 24**: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240.

## For example, 48, 96, 168 and 192 are all multiples of 24, 283 is not a multiple of 24 for the following reasons:

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

48 | 48÷24 = 2 | 48 is a multiple of 24 because it divides evenly. | 0 |

96 | 96÷24 = 4 | 96 is a multiple of 24 because it divides evenly. | 0 |

168 | 168÷24 = 7 | 168 is a multiple of 24 because it divides evenly. | 0 |

192 | 192÷24 = 8 | 192 is a multiple of 24 because it divides evenly. | 0 |

283 | 283÷24 = 11 | 283 is not a multiple of 24 because it does not divide evenly. | 19 |

## List of First 100 Multiples of 24 with Remainders

Number | Reason | Remainder |
---|---|---|

24 | 24 is a multiple of 24 because 24 × 1 = 24 | 0 |

48 | 48 is a multiple of 24 because 24 × 2 = 48 | 0 |

72 | 72 is a multiple of 24 because 24 × 3 = 72 | 0 |

96 | 96 is a multiple of 24 because 24 × 4 = 96 | 0 |

120 | 120 is a multiple of 24 because 24 × 5 = 120 | 0 |

144 | 144 is a multiple of 24 because 24 × 6 = 144 | 0 |

168 | 168 is a multiple of 24 because 24 × 7 = 168 | 0 |

192 | 192 is a multiple of 24 because 24 × 8 = 192 | 0 |

216 | 216 is a multiple of 24 because 24 × 9 = 216 | 0 |

240 | 240 is a multiple of 24 because 24 × 10 = 240 | 0 |

264 | 264 is a multiple of 24 because 24 × 11 = 264 | 0 |

288 | 288 is a multiple of 24 because 24 × 12 = 288 | 0 |

312 | 312 is a multiple of 24 because 24 × 13 = 312 | 0 |

336 | 336 is a multiple of 24 because 24 × 14 = 336 | 0 |

360 | 360 is a multiple of 24 because 24 × 15 = 360 | 0 |

384 | 384 is a multiple of 24 because 24 × 16 = 384 | 0 |

408 | 408 is a multiple of 24 because 24 × 17 = 408 | 0 |

432 | 432 is a multiple of 24 because 24 × 18 = 432 | 0 |

456 | 456 is a multiple of 24 because 24 × 19 = 456 | 0 |

480 | 480 is a multiple of 24 because 24 × 20 = 480 | 0 |

504 | 504 is a multiple of 24 because 24 × 21 = 504 | 0 |

528 | 528 is a multiple of 24 because 24 × 22 = 528 | 0 |

552 | 552 is a multiple of 24 because 24 × 23 = 552 | 0 |

576 | 576 is a multiple of 24 because 24 × 24 = 576 | 0 |

600 | 600 is a multiple of 24 because 24 × 25 = 600 | 0 |

624 | 624 is a multiple of 24 because 24 × 26 = 624 | 0 |

648 | 648 is a multiple of 24 because 24 × 27 = 648 | 0 |

672 | 672 is a multiple of 24 because 24 × 28 = 672 | 0 |

696 | 696 is a multiple of 24 because 24 × 29 = 696 | 0 |

720 | 720 is a multiple of 24 because 24 × 30 = 720 | 0 |

744 | 744 is a multiple of 24 because 24 × 31 = 744 | 0 |

768 | 768 is a multiple of 24 because 24 × 32 = 768 | 0 |

792 | 792 is a multiple of 24 because 24 × 33 = 792 | 0 |

816 | 816 is a multiple of 24 because 24 × 34 = 816 | 0 |

840 | 840 is a multiple of 24 because 24 × 35 = 840 | 0 |

864 | 864 is a multiple of 24 because 24 × 36 = 864 | 0 |

888 | 888 is a multiple of 24 because 24 × 37 = 888 | 0 |

912 | 912 is a multiple of 24 because 24 × 38 = 912 | 0 |

936 | 936 is a multiple of 24 because 24 × 39 = 936 | 0 |

960 | 960 is a multiple of 24 because 24 × 40 = 960 | 0 |

984 | 984 is a multiple of 24 because 24 × 41 = 984 | 0 |

1008 | 1008 is a multiple of 24 because 24 × 42 = 1008 | 0 |

1032 | 1032 is a multiple of 24 because 24 × 43 = 1032 | 0 |

1056 | 1056 is a multiple of 24 because 24 × 44 = 1056 | 0 |

1080 | 1080 is a multiple of 24 because 24 × 45 = 1080 | 0 |

1104 | 1104 is a multiple of 24 because 24 × 46 = 1104 | 0 |

1128 | 1128 is a multiple of 24 because 24 × 47 = 1128 | 0 |

1152 | 1152 is a multiple of 24 because 24 × 48 = 1152 | 0 |

1176 | 1176 is a multiple of 24 because 24 × 49 = 1176 | 0 |

1200 | 1200 is a multiple of 24 because 24 × 50 = 1200 | 0 |

1224 | 1224 is a multiple of 24 because 24 × 51 = 1224 | 0 |

1248 | 1248 is a multiple of 24 because 24 × 52 = 1248 | 0 |

1272 | 1272 is a multiple of 24 because 24 × 53 = 1272 | 0 |

1296 | 1296 is a multiple of 24 because 24 × 54 = 1296 | 0 |

1320 | 1320 is a multiple of 24 because 24 × 55 = 1320 | 0 |

1344 | 1344 is a multiple of 24 because 24 × 56 = 1344 | 0 |

1368 | 1368 is a multiple of 24 because 24 × 57 = 1368 | 0 |

1392 | 1392 is a multiple of 24 because 24 × 58 = 1392 | 0 |

1416 | 1416 is a multiple of 24 because 24 × 59 = 1416 | 0 |

1440 | 1440 is a multiple of 24 because 24 × 60 = 1440 | 0 |

1464 | 1464 is a multiple of 24 because 24 × 61 = 1464 | 0 |

1488 | 1488 is a multiple of 24 because 24 × 62 = 1488 | 0 |

1512 | 1512 is a multiple of 24 because 24 × 63 = 1512 | 0 |

1536 | 1536 is a multiple of 24 because 24 × 64 = 1536 | 0 |

1560 | 1560 is a multiple of 24 because 24 × 65 = 1560 | 0 |

1584 | 1584 is a multiple of 24 because 24 × 66 = 1584 | 0 |

1608 | 1608 is a multiple of 24 because 24 × 67 = 1608 | 0 |

1632 | 1632 is a multiple of 24 because 24 × 68 = 1632 | 0 |

1656 | 1656 is a multiple of 24 because 24 × 69 = 1656 | 0 |

1680 | 1680 is a multiple of 24 because 24 × 70 = 1680 | 0 |

1704 | 1704 is a multiple of 24 because 24 × 71 = 1704 | 0 |

1728 | 1728 is a multiple of 24 because 24 × 72 = 1728 | 0 |

1752 | 1752 is a multiple of 24 because 24 × 73 = 1752 | 0 |

1776 | 1776 is a multiple of 24 because 24 × 74 = 1776 | 0 |

1800 | 1800 is a multiple of 24 because 24 × 75 = 1800 | 0 |

1824 | 1824 is a multiple of 24 because 24 × 76 = 1824 | 0 |

1848 | 1848 is a multiple of 24 because 24 × 77 = 1848 | 0 |

1872 | 1872 is a multiple of 24 because 24 × 78 = 1872 | 0 |

1896 | 1896 is a multiple of 24 because 24 × 79 = 1896 | 0 |

1920 | 1920 is a multiple of 24 because 24 × 80 = 1920 | 0 |

1944 | 1944 is a multiple of 24 because 24 × 81 = 1944 | 0 |

1968 | 1968 is a multiple of 24 because 24 × 82 = 1968 | 0 |

1992 | 1992 is a multiple of 24 because 24 × 83 = 1992 | 0 |

2016 | 2016 is a multiple of 24 because 24 × 84 = 2016 | 0 |

2040 | 2040 is a multiple of 24 because 24 × 85 = 2040 | 0 |

2064 | 2064 is a multiple of 24 because 24 × 86 = 2064 | 0 |

2088 | 2088 is a multiple of 24 because 24 × 87 = 2088 | 0 |

2112 | 2112 is a multiple of 24 because 24 × 88 = 2112 | 0 |

2136 | 2136 is a multiple of 24 because 24 × 89 = 2136 | 0 |

2160 | 2160 is a multiple of 24 because 24 × 90 = 2160 | 0 |

2184 | 2184 is a multiple of 24 because 24 × 91 = 2184 | 0 |

2208 | 2208 is a multiple of 24 because 24 × 92 = 2208 | 0 |

2232 | 2232 is a multiple of 24 because 24 × 93 = 2232 | 0 |

2256 | 2256 is a multiple of 24 because 24 × 94 = 2256 | 0 |

2280 | 2280 is a multiple of 24 because 24 × 95 = 2280 | 0 |

2304 | 2304 is a multiple of 24 because 24 × 96 = 2304 | 0 |

2328 | 2328 is a multiple of 24 because 24 × 97 = 2328 | 0 |

2352 | 2352 is a multiple of 24 because 24 × 98 = 2352 | 0 |

2376 | 2376 is a multiple of 24 because 24 × 99 = 2376 | 0 |

2400 | 2400 is a multiple of 24 because 24 × 100 = 2400 | 0 |

## Read More About Multiples of 24

## Important Notes

### 1. Definition of Multiples

Multiples of a number are obtained by multiplying that number by integers. For instance, multiples of 24 are the results of 24 multiplied by 1, 2, 3, etc.

### 2. First Ten Multiples of 24

Here are the first ten multiples of 24:

- 24 × 1 = 24
- 24 × 2 = 48
- 24 × 3 = 72
- 24 × 4 = 96
- 24 × 5 = 120
- 24 × 6 = 144
- 24 × 7 = 168
- 24 × 8 = 192
- 24 × 9 = 216
- 24 × 10 = 240

### 3. Characteristics of Multiples of 24

**Even Numbers:**All multiples of 24 are even because 24 itself is an even number.**Divisibility:**Each multiple of 24 is divisible by 2, 3, 4, 6, 8, and 12.

### 4. Patterns in Multiples

Multiples of 24 increase by 24. This means each subsequent multiple is 24 units more than the previous one. For example:

- 24, 48, 72, 96, …

### 5. Real-Life Applications

**Time Measurement:**24 is significant in timekeeping (24 hours in a day).**Mathematical Problems:**Multiples of 24 are used in problems involving least common multiples, greatest common divisors, and finding common denominators in fractions.

## Examples on Multiples of 24

### Example 1: Finding Multiples of 24

To find the first five multiples of 24:

- 24×1 = 24
- 24×2 = 48
- 24×3 = 72
- 24×4 = 96
- 24×5 = 120

### Example 2: Real-Life Application – Packaging

A factory packs products in boxes containing 24 items each. If the factory packs 10 boxes, how many items are packed in total?

24×10 = 240 So, 240 items are packed in total.

### Example 3: Scheduling

A conference is scheduled every 24 days. If the first conference is on January 1st, when will the next three conferences be held?

- First conference: January 1
- Second conference: January 1 + 24 days = January 25
- Third conference: January 25 + 24 days = February 18
- Fourth conference: February 18 + 24 days = March 13

### Example 4: Financial Planning

An investor receives a dividend every 24 weeks. If the first dividend was received on January 1st, when will the investor receive the next three dividends?

- First dividend: January 1
- Second dividend: January 1 + 24 weeks = June 17
- Third dividend: June 17 + 24 weeks = December 2
- Fourth dividend: December 2 + 24 weeks = May 17 (next year)

### Example 5: Sports Tournament

A sports league schedules matches every 24 days. If a match is played on February 1st, what are the dates of the next two matches?

- First match: February 1
- Second match: February 1 + 24 days = February 25
- Third match: February 25 + 24 days = March 20

### Table of First 10 Multiples of 24

Multiple | Value |
---|---|

24 × 1 | 24 |

24 × 2 | 48 |

24 × 3 | 72 |

24 × 4 | 96 |

24 × 5 | 120 |

24 × 6 | 144 |

24 × 7 | 168 |

24 × 8 | 192 |

24 × 9 | 216 |

24 × 10 | 240 |

## FAQs

## What are multiples of 24?

Multiples of 24 are numbers that can be expressed as 24 times an integer. Examples include 24, 48, 72, 96, 120, etc.

## Is 120 a multiple of 24?

Yes, 120 is a multiple of 24 because 120 ÷ 24 equals 5, an integer.

## What is the smallest multiple of 24?

The smallest multiple of 24 is 24 itself.

## Are all multiples of 24 even numbers?

Yes, since 24 is an even number, all multiples of 24 are also even numbers.

## How can you determine if a number is a multiple of 24?

A number is a multiple of 24 if it can be divided by 24 without leaving a remainder.

## What is the 5th multiple of 24?

The 5th multiple of 24 is 120 (24 × 5).

## Are multiples of 24 also multiples of 12?

Yes, since 24 is a multiple of 12, all multiples of 24 are also multiples of 12.

## Can a negative number be a multiple of 24?

Yes, negative numbers can be multiples of 24, such as -24, -48, -72, etc.

## What is the greatest common divisor (GCD) of 24 and its multiples?

The GCD of 24 and any of its multiples is always 24.

## Are multiples of 24 always divisible by 8?

Yes, since 24 is divisible by 8, all multiples of 24 are also divisible by 8.