Multiples of 8
Multiples of 8
Multiples of 8 are the products of the integer 8 and any whole number. In mathematics, these multiples are generated through multiplication, resulting in numbers such as 8, 16, 24, and so on. Each multiple of 8 is an integer that can be evenly divided by 8, making 8 one of its divisors. Understanding multiples helps in identifying factors and divisors in number theory. Recognizing multiples of 8 is fundamental in various mathematical applications and problem-solving.
What are Multiples of 8?
Multiples of 8 are numbers that can be expressed as 8 times an integer, such as 8, 16, 24, 32, and so on. They are the results of multiplying 8 by any whole number.
For example, 16, 40, 56 and 64 are all multiples of 8, 25 is not a multiple of 8 for the following reasons:
| Number | Reason | Remainder |
|---|---|---|
| 16 | 16 ÷ 8 = 2, which is an integer | 0 |
| 40 | 40 ÷ 8 = 5, which is an integer | 0 |
| 56 | 56 ÷ 8 = 7, which is an integer | 0 |
| 64 | 64 ÷ 8 = 8, which is an integer | 0 |
| 25 | 25 ÷ 8 = 3.125, which is not an integer | 1 |
List of First 100 Multiples of 8 with Remainders
| Number | Reason | Remainder |
|---|---|---|
| 8 | 8 ÷ 8 = 1, which is an integer | 0 |
| 16 | 16 ÷ 8 = 2, which is an integer | 0 |
| 24 | 24 ÷ 8 = 3, which is an integer | 0 |
| 32 | 32 ÷ 8 = 4, which is an integer | 0 |
| 40 | 40 ÷ 8 = 5, which is an integer | 0 |
| 48 | 48 ÷ 8 = 6, which is an integer | 0 |
| 56 | 56 ÷ 8 = 7, which is an integer | 0 |
| 64 | 64 ÷ 8 = 8, which is an integer | 0 |
| 72 | 72 ÷ 8 = 9, which is an integer | 0 |
| 80 | 80 ÷ 8 = 10, which is an integer | 0 |
| 88 | 88 ÷ 8 = 11, which is an integer | 0 |
| 96 | 96 ÷ 8 = 12, which is an integer | 0 |
| 104 | 104 ÷ 8 = 13, which is an integer | 0 |
| 112 | 112 ÷ 8 = 14, which is an integer | 0 |
| 120 | 120 ÷ 8 = 15, which is an integer | 0 |
| 128 | 128 ÷ 8 = 16, which is an integer | 0 |
| 136 | 136 ÷ 8 = 17, which is an integer | 0 |
| 144 | 144 ÷ 8 = 18, which is an integer | 0 |
| 152 | 152 ÷ 8 = 19, which is an integer | 0 |
| 160 | 160 ÷ 8 = 20, which is an integer | 0 |
| 168 | 168 ÷ 8 = 21, which is an integer | 0 |
| 176 | 176 ÷ 8 = 22, which is an integer | 0 |
| 184 | 184 ÷ 8 = 23, which is an integer | 0 |
| 192 | 192 ÷ 8 = 24, which is an integer | 0 |
| 200 | 200 ÷ 8 = 25, which is an integer | 0 |
| 208 | 208 ÷ 8 = 26, which is an integer | 0 |
| 216 | 216 ÷ 8 = 27, which is an integer | 0 |
| 224 | 224 ÷ 8 = 28, which is an integer | 0 |
| 232 | 232 ÷ 8 = 29, which is an integer | 0 |
| 240 | 240 ÷ 8 = 30, which is an integer | 0 |
| 248 | 248 ÷ 8 = 31, which is an integer | 0 |
| 256 | 256 ÷ 8 = 32, which is an integer | 0 |
| 264 | 264 ÷ 8 = 33, which is an integer | 0 |
| 272 | 272 ÷ 8 = 34, which is an integer | 0 |
| 280 | 280 ÷ 8 = 35, which is an integer | 0 |
| 288 | 288 ÷ 8 = 36, which is an integer | 0 |
| 296 | 296 ÷ 8 = 37, which is an integer | 0 |
| 304 | 304 ÷ 8 = 38, which is an integer | 0 |
| 312 | 312 ÷ 8 = 39, which is an integer | 0 |
| 320 | 320 ÷ 8 = 40, which is an integer | 0 |
| 328 | 328 ÷ 8 = 41, which is an integer | 0 |
| 336 | 336 ÷ 8 = 42, which is an integer | 0 |
| 344 | 344 ÷ 8 = 43, which is an integer | 0 |
| 352 | 352 ÷ 8 = 44, which is an integer | 0 |
| 360 | 360 ÷ 8 = 45, which is an integer | 0 |
| 368 | 368 ÷ 8 = 46, which is an integer | 0 |
| 376 | 376 ÷ 8 = 47, which is an integer | 0 |
| 384 | 384 ÷ 8 = 48, which is an integer | 0 |
| 392 | 392 ÷ 8 = 49, which is an integer | 0 |
| 400 | 400 ÷ 8 = 50, which is an integer | 0 |
| 408 | 408 ÷ 8 = 51, which is an integer | 0 |
| 416 | 416 ÷ 8 = 52, which is an integer | 0 |
| 424 | 424 ÷ 8 = 53, which is an integer | 0 |
| 432 | 432 ÷ 8 = 54, which is an integer | 0 |
| 440 | 440 ÷ 8 = 55, which is an integer | 0 |
| 448 | 448 ÷ 8 = 56, which is an integer | 0 |
| 456 | 456 ÷ 8 = 57, which is an integer | 0 |
| 464 | 464 ÷ 8 = 58, which is an integer | 0 |
| 472 | 472 ÷ 8 = 59, which is an integer | 0 |
| 480 | 480 ÷ 8 = 60, which is an integer | 0 |
| 488 | 488 ÷ 8 = 61, which is an integer | 0 |
| 496 | 496 ÷ 8 = 62, which is an integer | 0 |
| 504 | 504 ÷ 8 = 63, which is an integer | 0 |
| 512 | 512 ÷ 8 = 64, which is an integer | 0 |
| 520 | 520 ÷ 8 = 65, which is an integer | 0 |
| 528 | 528 ÷ 8 = 66, which is an integer | 0 |
| 536 | 536 ÷ 8 = 67, which is an integer | 0 |
| 544 | 544 ÷ 8 = 68, which is an integer | 0 |
| 552 | 552 ÷ 8 = 69, which is an integer | 0 |
| 560 | 560 ÷ 8 = 70, which is an integer | 0 |
| 568 | 568 ÷ 8 = 71, which is an integer | 0 |
| 576 | 576 ÷ 8 = 72, which is an integer | 0 |
| 584 | 584 ÷ 8 = 73, which is an integer | 0 |
| 592 | 592 ÷ 8 = 74, which is an integer | 0 |
| 600 | 600 ÷ 8 = 75, which is an integer | 0 |
| 608 | 608 ÷ 8 = 76, which is an integer | 0 |
| 616 | 616 ÷ 8 = 77, which is an integer | 0 |
| 624 | 624 ÷ 8 = 78, which is an integer | 0 |
| 632 | 632 ÷ 8 = 79, which is an integer | 0 |
| 640 | 640 ÷ 8 = 80, which is an integer | 0 |
| 648 | 648 ÷ 8 = 81, which is an integer | 0 |
| 656 | 656 ÷ 8 = 82, which is an integer | 0 |
| 664 | 664 ÷ 8 = 83, which is an integer | 0 |
| 672 | 672 ÷ 8 = 84, which is an integer | 0 |
| 680 | 680 ÷ 8 = 85, which is an integer | 0 |
| 688 | 688 ÷ 8 = 86, which is an integer | 0 |
| 696 | 696 ÷ 8 = 87, which is an integer | 0 |
| 704 | 704 ÷ 8 = 88, which is an integer | 0 |
| 712 | 712 ÷ 8 = 89, which is an integer | 0 |
| 720 | 720 ÷ 8 = 90, which is an integer | 0 |
| 728 | 728 ÷ 8 = 91, which is an integer | 0 |
| 736 | 736 ÷ 8 = 92, which is an integer | 0 |
| 744 | 744 ÷ 8 = 93, which is an integer | 0 |
| 752 | 752 ÷ 8 = 94, which is an integer | 0 |
| 760 | 760 ÷ 8 = 95, which is an integer | 0 |
| 768 | 768 ÷ 8 = 96, which is an integer | 0 |
| 776 | 776 ÷ 8 = 97, which is an integer | 0 |
| 784 | 784 ÷ 8 = 98, which is an integer | 0 |
| 792 | 792 ÷ 8 = 99, which is an integer | 0 |
| 800 | 800 ÷ 8 = 100, which is an integer | 0 |
Important Notes
Definition of Multiples of 8
Multiples of 8 are numbers that can be expressed as the product of 8 and any integer. In other words, a multiple of 8 can be written in the form: 8n8n8n where nnn is an integer (positive, negative, or zero).
Identifying Multiples of 8
To find multiples of 8, you multiply 8 by integers. Here are the first ten multiples of 8:
- 8×1 = 8
- 8×2 = 16
- 8×3 = 24
- 8×4 = 32
- 8×5 = 40
- 8×6 = 48
- 8×7 = 56
- 8×8 = 64
- 8×9 = 72
- 8×10 = 80
Properties of Multiples of 8
- Divisibility: A number is a multiple of 8 if the last three digits of the number form a number that is divisible by 8. For example, 1,024 is a multiple of 8 because 024 (the last three digits) is divisible by 8.
- Even Numbers: All multiples of 8 are even because they end in an even digit (0, 2, 4, 6, or 8).
Practical Applications
- LCM (Least Common Multiple): Multiples of 8 are often used to find the LCM of numbers, especially when working with multiples of other numbers.
- Problem Solving: Knowing multiples of 8 helps in solving problems related to grouping, distribution, and finding patterns in sequences.
Common Examples and Practice
Example 1: Identify if 1,024 is a multiple of 8.
Check the last three digits: 024. Since 024 is divisible by 8, 1,024 is a multiple of 8.
Example 2: Find the multiple of 8 that lies between 90 and 110.
The multiples of 8 around this range are 88 and 96. So, 96 is the multiple of 8 between 90 and 110.
Table of Multiples of 8 (1-10)
| n | Multiple of 8 |
|---|---|
| 1 | 8 |
| 2 | 16 |
| 3 | 24 |
| 4 | 32 |
| 5 | 40 |
| 6 | 48 |
| 7 | 56 |
| 8 | 64 |
| 9 | 72 |
| 10 | 80 |
Examples on Multiples of 8
Example 1: Identifying a Multiple of 8
Problem: Determine if 192 is a multiple of 8.
Solution: To check if 192 is a multiple of 8, we can use the divisibility rule for 8: a number is a multiple of 8 if the last three digits are divisible by 8. Since 192 has only three digits, we use the whole number.
- Divide 192 by 8: 192÷8 = 24
- Since 24 is an integer, 192 is a multiple of 8.
Yes, 192 is a multiple of 8.
Example 2: Finding the 15th Multiple of 8
Problem: Find the 15th multiple of 8.
Solution: To find the 15th multiple of 8, multiply 8 by 15.
- Calculation: 8×15 = 120
The 15th multiple of 8 is 120.
Example 3: Real-World Application
Problem: A factory packs 8 bottles in each box. How many boxes are needed to pack 1,024 bottles?
Solution: To find out how many boxes are needed, divide the total number of bottles by the number of bottles per box.
- Calculation: 1,024÷8 = 128
The factory needs 128 boxes to pack 1,024 bottles.
Practical Examples of Multiples of 8
Example 1: Packing in Bulk
Scenario: A warehouse needs to pack toys into boxes. Each box can hold 8 toys. How many boxes are needed to pack 200 toys?
Solution: To determine the number of boxes required, divide the total number of toys by the capacity of one box.
- Calculation: 200÷8 = 25
25 boxes are needed to pack 200 toys.
Example 2: Event Seating Arrangement
Scenario: An event planner is arranging seats for a conference. Each row must have 8 chairs. If there are 320 attendees, how many rows of chairs are needed?
Solution: To find the number of rows needed, divide the total number of attendees by the number of chairs per row.
- Calculation: 320÷8 = 40
40 rows of chairs are needed for 320 attendees.
Example 3: Budgeting for Supplies
Scenario: A school needs to buy notebooks for students. Notebooks come in packs of 8. If the school needs 1,200 notebooks, how many packs should they purchase?
Solution: To determine the number of packs required, divide the total number of notebooks by the number of notebooks per pack.
- Calculation: 1,200÷8 = 150
The school should purchase 150 packs of notebooks.
FAQs
What is a multiple of 8?
A multiple of 8 is a number that can be expressed as 8 times an integer. In other words, it is the product of 8 and any whole number (positive, negative, or zero). For example, 8, 16, and 24 are multiples of 8.
How do you determine if a number is a multiple of 8?
To determine if a number is a multiple of 8, check if the last three digits of the number form a number that is divisible by 8. Alternatively, you can divide the number by 8 and see if the result is an integer. If it is, the number is a multiple of 8.
What are the first ten multiples of 8?
The first ten multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
Are all multiples of 8 also multiples of 4?
Yes, all multiples of 8 are also multiples of 4. This is because 8 is itself a multiple of 4 (8 = 4 × 2). Therefore, any number that is a multiple of 8 can also be expressed as a multiple of 4.
How can multiples of 8 be used in real life?
Multiples of 8 can be used in various real-life scenarios such as packaging, event planning, and budgeting. For instance, if items are packed in groups of 8, knowing multiples of 8 helps determine the number of packages needed for a given quantity of items.
Is zero considered a multiple of 8?
Yes, zero is considered a multiple of 8 because any number multiplied by zero is zero. Therefore, 8 × 0 = 0, making zero a multiple of 8.
Can a negative number be a multiple of 8?
Yes, negative numbers can be multiples of 8. For example, -8, -16, and -24 are multiples of 8 because they can be expressed as 8 multiplied by a negative integer (e.g., 8 × -1 = -8).
What is the least common multiple (LCM) of 8 and 12?
The least common multiple (LCM) of 8 and 12 is 24. This is the smallest number that is a multiple of both 8 and 12.
How can you use multiples of 8 to simplify fractions?
To simplify fractions, you can use multiples of 8 by finding a common multiple or factor. For example, to simplify 16/24, recognize that both 16 and 24 are multiples of 8. Divide both numerator and denominator by 8 to get 2/3.
What is the 20th multiple of 8?
The 20th multiple of 8 is found by multiplying 8 by 20.
Calculation: 8 × 20 = 160
The 20th multiple of 8 is 160.
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