Multiples of 4
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.
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
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