# Multiples of 28

Created by: Team Maths - Examples.com, Last Updated: July 31, 2024

## Multiples of 28

Multiples of 28 refer to the numbers obtained by multiplying 28 by various integers. In mathematics, a multiple is a product of a given number and an integer. For instance, 28 multiplied by 1, 2, 3, and so on results in its multiples: 28, 56, 84, etc. These numbers share common divisors and factors, making them integral to understanding number theory and multiplication principles. Identifying multiples of 28 helps in solving problems related to divisors and factors in integer mathematics.

## What are Multiples of 28?

Multiples of 28 are the numbers that result from multiplying 28 by any whole number. They follow the pattern 28, 56, 84, 112, and so on. In general, the nth multiple of 28 can be represented as 28n, where n is a positive integer.

Prime Factorization of 28: 28 = 2² × 7 First 10 multiples of 28: 28, 56, 84, 112, 140, 168, 196, 224, 252, 280.

Table of 28

## Important Notes

### Step 1: Definition of Multiples

Multiples of a number are the products of that number and any integer. For example, the multiples of 28 are found by multiplying 28 by integers such as 1, 2, 3, etc.

### Step 2: First Ten Multiples of 28

The first ten multiples of 28 are:

• 28×1 = 28
• 28×2 = 56
• 28×3 = 84
• 28×4 = 112
• 28×5 = 140
• 28×6 = 168
• 28×7 = 196
• 28×8 = 224
• 28×9 = 252
• 28×10 = 280

### Step 3: Common Characteristics

• Even Numbers: All multiples of 28 are even because 28 is an even number.
• Divisibility by 4 and 7: Since 28 is divisible by both 4 and 7, all multiples of 28 are also divisible by 4 and 7.

### Step 4: Least Common Multiple (LCM)

The LCM of two numbers is the smallest number that is a multiple of both. For instance, the LCM of 28 and another number can be found using the prime factorization method.

### Step 5: Applications

• Mathematics Problems: Multiples are useful in solving problems involving patterns, sequences, and factors.
• Real-Life Scenarios: Understanding multiples can help in scheduling events, distributing items evenly, and more.

## Examples on Multiples of 28

### Example 1: Finding the Least Common Multiple (LCM)

Problem: Find the LCM of 28 and 35.

List the prime factors of each number:

• 28 = 2 × 2 × 7
• 35 = 5 × 7

Identify the highest power of each prime factor:

• Prime factors: 2, 5, 7
• Highest powers: 222², 515¹, 717¹

Multiply these highest powers:

• LCM = 22²×5¹×7¹
• LCM = 4 × 5 × 7 = 140

The LCM of 28 and 35 is 140.

### Example 2: Word Problem Involving Multiples

Problem: Sarah is organizing gift bags. Each bag must contain either 28 or 56 candies. If she has 280 candies, how many bags of each type can she make?

Determine the multiples:

• 28 × 10 = 280 (for bags containing 28 candies)
• 56 × 5 = 280 (for bags containing 56 candies)

Possible combinations:

• She can make 10 bags with 28 candies each, or
• She can make 5 bags with 56 candies each.

Sarah can make 10 bags with 28 candies each or 5 bags with 56 candies each.

### Example 3: Practical Application in Scheduling

Problem: A train runs every 28 minutes. If the first train leaves at 6:00 AM, at what times will the train depart within the next 4 hours?

List the multiples of 28 within 240 minutes (4 hours):

• 28, 56, 84, 112, 140, 168, 196, 224

Convert these to time:

• 6:00 AM + 28 minutes = 6:28 AM
• 6:00 AM + 56 minutes = 6:56 AM
• 6:00 AM + 84 minutes = 7:24 AM
• 6:00 AM + 112 minutes = 7:52 AM
• 6:00 AM + 140 minutes = 8:20 AM
• 6:00 AM + 168 minutes = 8:48 AM
• 6:00 AM + 196 minutes = 9:16 AM
• 6:00 AM + 224 minutes = 9:44 AM

The train will depart at 6:28 AM, 6:56 AM, 7:24 AM, 7:52 AM, 8:20 AM, 8:48 AM, 9:16 AM, and 9:44 AM.

### Example 4: Divisibility Check

Problem: Is 196 a multiple of 28?

Divide 196 by 28:

• 196÷28 = 7

Since the quotient is a whole number, 196 is a multiple of 28.

Yes, 196 is a multiple of 28.

### Example 5: Construction Project

Problem: A contractor needs to purchase packs of tiles, with each pack containing 28 tiles. If the project requires 420 tiles, how many packs are needed?

Divide the total number of tiles by the number of tiles per pack:

420÷28 = 15

The contractor needs 15 packs of tiles.

## What are multiples of 28?

Multiples of 28 are numbers that can be expressed as 28 times an integer, such as 28, 56, 84, 112, and so on.

## Is 140 a multiple of 28?

Yes, 140 is a multiple of 28 because 28 times 5 equals 140.

## How can I find the 10th multiple of 28?

To find the 10th multiple of 28, multiply 28 by 10, which equals 280.

## Are all multiples of 28 even numbers?

Yes, all multiples of 28 are even numbers because 28 itself is an even number.

## Can a multiple of 28 be a prime number?

No, a multiple of 28 cannot be a prime number because it has factors other than 1 and itself.

## What is the least common multiple (LCM) of 28 and 42?

The least common multiple of 28 and 42 is 84.

## Are 56 and 84 multiples of 28?

Yes, both 56 and 84 are multiples of 28 because 28 times 2 equals 56 and 28 times 3 equals 84.

## How do I determine if a number is a multiple of 28?

To determine if a number is a multiple of 28, divide the number by 28. If the result is an integer, it is a multiple of 28.

## What are the first five multiples of 28?

The first five multiples of 28 are 28, 56, 84, 112, and 140.

## Is 280 the greatest multiple of 28 under 300?

Yes, 280 is the greatest multiple of 28 under 300 because 28 times 10 equals 280 and 28 times 11 equals 308, which is over 300.

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