# Multiples of 4

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

## 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

## List of First 100 Multiples of 4 with Remainders

table with detailed content inside each calculation cell:

Table 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.

## 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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