# Multiples of 8

Created by: Team Maths - Examples.com, Last Updated: August 21, 2024

## 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.

Prime factorization of 8: 8 = 2 × 2 × 2 = 2³ First 10 multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80.

Table of 8

## 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.

## 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.

## 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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