## Multiples of 4

Multiples of 4 are numbers that result from multiplying 4 by any integer. In mathematics, these numbers, such as 4, 8, 12, and 16, are the product of 4 and another whole number. The concept involves understanding factors and divisors, as a multiple of 4 can be evenly divided by 4 without a remainder. Identifying multiples is essential in various mathematical applications, including finding common multiples and solving divisibility problems.

## What are Multiples of 4?

Multiples of 4 are numbers that result from multiplying 4 by any integer. **These numbers include 4, 8, 12, 16, and so on, forming a sequence where each number is the product of 4 and a whole number.** In other words, a multiple of 4 is any number that can be divided evenly by 4 without leaving a remainder.

**Prime factorization of 4:**4 = 2 × 2 = 2²

**First 10 Multiples of 4:**4, 8, 12, 16, 20, 24, 28, 32, 36, 40

**First 50 Multiples of 4 are**4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

## For example, 16, 20, 40 are all multiples of 4, 47 is not a multiple of 4 for the following reasons:

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

16 | 16 ÷ 4 = 4 | 0 |

20 | 20 ÷ 4 = 5 | 0 |

40 | 40 ÷ 4 = 10 | 0 |

47 | 47 ÷ 4 = 11.75 | 3 |

## List of First 100 Multiples of 4 with Remainders

table with detailed content inside each calculation cell:

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

4 | 4÷4 = 1, so 4 is divisible by 4. | 0 |

8 | 8÷4 = 2, so 8 is divisible by 4. | 0 |

12 | 12÷4 = 3, so 12 is divisible by 4. | 0 |

16 | 16÷4 = 4, so 16 is divisible by 4. | 0 |

20 | 20÷4 = 5, so 20 is divisible by 4. | 0 |

24 | 24÷4 = 6, so 24 is divisible by 4. | 0 |

28 | 28÷4 = 7, so 28 is divisible by 4. | 0 |

32 | 32÷4 = 8, so 32 is divisible by 4. | 0 |

36 | 36÷4 = 9, so 36 is divisible by 4. | 0 |

40 | 40÷4 = 10, so 40 is divisible by 4. | 0 |

44 | 44÷4 = 11, so 44 is divisible by 4. | 0 |

48 | 48÷4 = 12, so 48 is divisible by 4. | 0 |

52 | 52÷4 = 13, so 52 is divisible by 4. | 0 |

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

60 | 60÷4 = 15, so 60 is divisible by 4. | 0 |

64 | 64÷4 = 16, so 64 is divisible by 4. | 0 |

68 | 68÷4 = 17, so 68 is divisible by 4. | 0 |

72 | 72÷4 = 18, so 72 is divisible by 4. | 0 |

76 | 76÷4 = 19, so 76 is divisible by 4. | 0 |

80 | 80÷4 = 20, so 80 is divisible by 4. | 0 |

84 | 84÷4 = 21, so 84 is divisible by 4. | 0 |

88 | 88÷4 = 22, so 88 is divisible by 4. | 0 |

92 | 92÷4 = 23, so 92 is divisible by 4. | 0 |

96 | 96÷4 = 24, so 96 is divisible by 4. | 0 |

100 | 100÷4 = 25, so 100 is divisible by 4. | 0 |

104 | 104÷4 = 26, so 104 is divisible by 4. | 0 |

108 | 108÷4 = 27, so 108 is divisible by 4. | 0 |

112 | 112÷4 = 28, so 112 is divisible by 4. | 0 |

116 | 116÷4 = 29, so 116 is divisible by 4. | 0 |

120 | 120÷4 = 30, so 120 is divisible by 4. | 0 |

124 | 124÷4 = 31, so 124 is divisible by 4. | 0 |

128 | 128÷4 = 32, so 128 is divisible by 4. | 0 |

132 | 132÷4 = 33, so 132 is divisible by 4. | 0 |

136 | 136÷4 = 34, so 136 is divisible by 4. | 0 |

140 | 140÷4 = 35, so 140 is divisible by 4. | 0 |

144 | 144÷4 = 36, so 144 is divisible by 4. | 0 |

148 | 148÷4 = 37, so 148 is divisible by 4. | 0 |

152 | 152÷4 = 38, so 152 is divisible by 4. | 0 |

156 | 156÷4 = 39, so 156 is divisible by 4. | 0 |

160 | 160÷4 = 40, so 160 is divisible by 4. | 0 |

164 | 164÷4 = 41, so 164 is divisible by 4. | 0 |

168 | 168÷4 = 42, so 168 is divisible by 4. | 0 |

172 | 172÷4 = 43, so 172 is divisible by 4. | 0 |

176 | 176÷4 = 44, so 176 is divisible by 4. | 0 |

180 | 180÷4 = 45, so 180 is divisible by 4. | 0 |

184 | 184÷4 = 46, so 184 is divisible by 4. | 0 |

188 | 188÷4 = 47, so 188 is divisible by 4. | 0 |

192 | 192÷4 = 48, so 192 is divisible by 4. | 0 |

196 | 196÷4 = 49, so 196 is divisible by 4. | 0 |

200 | 200÷4 = 50, so 200 is divisible by 4. | 0 |

204 | 204÷4 = 51, so 204 is divisible by 4. | 0 |

208 | 208÷4 = 52, so 208 is divisible by 4. | 0 |

212 | 212÷4 = 53, so 212 is divisible by 4. | 0 |

216 | 216÷4 = 54, so 216 is divisible by 4. | 0 |

220 | 220÷4 = 55, so 220 is divisible by 4. | 0 |

224 | 224÷4 = 56, so 224 is divisible by 4. | 0 |

228 | 228÷4 = 57, so 228 is divisible by 4. | 0 |

232 | 232÷4 = 58, so 232 is divisible by 4. | 0 |

236 | 236÷4 = 59, so 236 is divisible by 4. | 0 |

240 | 240÷4 = 60, so 240 is divisible by 4. | 0 |

244 | 244÷4 = 61, so 244 is divisible by 4. | 0 |

248 | 248÷4 = 62, so 248 is divisible by 4. | 0 |

252 | 252÷4 = 63, so 252 is divisible by 4. | 0 |

256 | 256÷4 = 64, so 256 is divisible by 4. | 0 |

260 | 260÷4 = 65, so 260 is divisible by 4. | 0 |

264 | 264÷4 = 66, so 264 is divisible by 4. | 0 |

268 | 268÷4 = 67, so 268 is divisible by 4. | 0 |

272 | 272÷4 = 68, so 272 is divisible by 4. | 0 |

276 | 276÷4 = 69, so 276 is divisible by 4. | 0 |

280 | 280÷4 = 70, so 280 is divisible by 4. | 0 |

284 | 284÷4 = 71, so 284 is divisible by 4. | 0 |

288 | 288÷4 = 72, so 288 is divisible by 4. | 0 |

292 | 292÷4 = 73, so 292 is divisible by 4. | 0 |

296 | 296÷4 = 74, so 296 is divisible by 4. | 0 |

300 | 300÷4 = 75, so 300 is divisible by 4. | 0 |

304 | 304÷4 = 76, so 304 is divisible by 4. | 0 |

308 | 308÷4 = 77, so 308 is divisible by 4. | 0 |

312 | 312÷4 = 78, so 312 is divisible by 4. | 0 |

316 | 316÷4 = 79, so 316 is divisible by 4. | 0 |

320 | 320÷4 = 80, so 320 is divisible by 4. | 0 |

324 | 324÷4 = 81, so 324 is divisible by 4. | 0 |

328 | 328÷4 = 82, so 328 is divisible by 4. | 0 |

332 | 332÷4 = 83, so 332 is divisible by 4. | 0 |

336 | 336÷4 = 84, so 336 is divisible by 4. | 0 |

340 | 340÷4 = 85, so 340 is divisible by 4. | 0 |

344 | 344÷4 = 86, so 344 is divisible by 4. | 0 |

348 | 348÷4 = 87, so 348 is divisible by 4. | 0 |

352 | 352÷4 = 88, so 352 is divisible by 4. | 0 |

356 | 356÷4 = 89, so 356 is divisible by 4. | 0 |

360 | 360÷4 = 90, so 360 is divisible by 4. | 0 |

364 | 364÷4 = 91, so 364 is divisible by 4. | 0 |

368 | 368÷4 = 92, so 368 is divisible by 4. | 0 |

372 | 372÷4 = 93, so 372 is divisible by 4. | 0 |

376 | 376÷4 = 94, so 376 is divisible by 4. | 0 |

380 | 380÷4 = 95, so 380 is divisible by 4. | 0 |

384 | 384÷4 = 96, so 384 is divisible by 4. | 0 |

388 | 388÷4 = 97, so 388 is divisible by 4. | 0 |

392 | 392÷4 = 98, so 392 is divisible by 4. | 0 |

396 | 396÷4 = 99, so 396 is divisible by 4. | 0 |

400 | 400÷4 = 100, so 400 is divisible by 4. | 0 |

## Read More About Multiples of 4

## Important Notes

**Definition**: Multiples of 4 are numbers that result from multiplying 4 by any integer. Examples include 4, 8, 12, 16, and so on.**Divisibility**: A number is a multiple of 4 if it can be divided by 4 without leaving a remainder. For instance, 20 ÷ 4 = 5, so 20 is a multiple of 4.**Sequence**: The sequence of multiples of 4 is infinite, starting from 4 and continuing with 8, 12, 16, etc.**Applications**: Understanding multiples of 4 is useful in various mathematical problems, such as finding the least common multiple (LCM), solving division problems, and working with fractions.**Pattern Recognition**: Multiples of 4 follow a simple pattern: every fourth number in the natural number series is a multiple of 4, aiding in quick identification and calculations.

## Examples on Multiples of 4

### Example 1: Checking if a Number is a Multiple of 4

To determine if 32 is a multiple of 4, divide 32 by 4: 32÷4 = 8 Since the result is an integer with no remainder, 32 is a multiple of 4.

### Example 2: Finding Multiples of 4

To find the first five multiples of 4, multiply 4 by the first five integers:

- 4×1 = 4
- 4×2 = 8
- 4×3 = 12
- 4×4 = 16
- 4×5 = 20

Thus, the first five multiples of 4 are 4, 8, 12, 16, and 20.

### Example 3: Real-Life Application

Consider you have 48 apples, and you want to pack them into boxes, with 4 apples per box: 48÷4 = 12 You will have 12 boxes, showing that 48 is a multiple of 4.

### Example 4: Summing Multiples of 4

Find the sum of the multiples of 4 up to 20:

- Multiples: 4, 8, 12, 16, 20
- Sum: 4+8+12+16+20 = 60

Therefore, the sum of the multiples of 4 up to 20 is 60.

### Example 5: Multiples of 4 within a Range

Identify multiples of 4 between 10 and 30:

- Starting from 12 (the first multiple of 4 greater than 10)
- 12, 16, 20, 24, 28

## Practical Examples of Multiples of 4

### Example 1: Sharing Pencils

You have 24 pencils and want to distribute them equally among 4 students. Each student gets: 24÷4 = 6 So, 24 is a multiple of 4.

### Example 2: Packaging

A factory packs 4 bottles into each box. If there are 36 bottles, the number of boxes needed is: 36÷4 = 9 Therefore, 36 is a multiple of 4, requiring 9 boxes.

### Example 3: Time Management

If a task takes 4 minutes to complete, and you have 40 minutes available, you can complete the task: 40÷4 = 10 So, you can complete the task 10 times within 40 minutes, showing that 40 is a multiple of 4.

### Example 4: Arranging Chairs

You need to arrange 32 chairs in rows of 4. The number of rows will be: 32÷4 = 8 Thus, 32 is a multiple of 4, and you will have 8 rows.

### Example 5: Baking Cookies

A recipe calls for 4 eggs to make one batch of cookies. If you want to make 5 batches, you will need: 4×5 = 20 Therefore, you need 20 eggs, showing that 20 is a multiple of 4.

### Example 6: Financial Planning

You save $4 each day. After saving for 7 days, you will have: 4×7 = 28 So, you will have saved $28, which is a multiple of 4.

### Example 7: Classroom Groups

A teacher wants to divide 28 students into groups of 4. The number of groups will be: 28÷4 = 7 Therefore, 28 is a multiple of 4, resulting in 7 groups.

### Example 8: Exercise Routine

If you do 4 push-ups every set and plan to do 6 sets, the total number of push-ups will be: 4×6 = 24 Thus, you will do 24 push-ups, showing that 24 is a multiple of 4.

### Example 9: Building Blocks

A child has 16 building blocks and wants to build towers with 4 blocks each. The number of towers will be: 16÷4 = 4 Therefore, 16 is a multiple of 4, and the child can build 4 towers.

### Example 10: Grocery Shopping

A pack of water bottles contains 4 bottles. If you need 5 packs, the total number of bottles will be: 4×5 = 20 So, you will have 20 bottles, showing that 20 is a multiple of 4.

## FAQs

## What is a multiple of 4?

A multiple of 4 is any number that can be evenly divided by 4 without leaving a remainder. Examples include 4, 8, 12, 16, and so on.

## How can I determine if a number is a multiple of 4?

To determine if a number is a multiple of 4, divide the number by 4. If the result is a whole number with no remainder, then it is a multiple of 4.

## What are the first five multiples of 4?

The first five multiples of 4 are 4, 8, 12, 16, and 20.

## Are all multiples of 4 also multiples of other numbers?

Not necessarily. While some multiples of 4 might also be multiples of other numbers (e.g., 12 is a multiple of both 4 and 3), others may not be (e.g., 8 is only a multiple of 4 and 2).

## Why are multiples of 4 important in mathematics?

Multiples of 4 are important in mathematics for understanding patterns, solving problems involving divisibility, and finding the least common multiple (LCM) and greatest common divisor (GCD).

## Can negative numbers be multiples of 4?

Yes, negative numbers can also be multiples of 4. Examples include -4, -8, -12, and so on.

## How are multiples of 4 used in real life?

Multiples of 4 are used in various real-life applications such as packaging, time management, cooking, and organizing groups or items.

## Is zero considered a multiple of 4?

Yes, zero is considered a multiple of 4 because 0÷4 = 0 with no remainder.

## What is the rule for finding multiples of 4 using digit patterns?

A number is a multiple of 4 if the number formed by its last two digits is divisible by 4. For example, in 124, the last two digits form 24, which is divisible by 4, so 124 is a multiple of 4.

## What is the relationship between multiples of 4 and the number 2?

Multiples of 4 are also multiples of 2 because 4 itself is a multiple of 2 ( 4 = 2×2 ). Therefore, any multiple of 4 can be evenly divided by 2