# Multiples of 26

Created by: Team Maths - Examples.com, Last Updated: May 24, 2024

## Multiples of 26

Multiples of 26 are integers that result from multiplying 26 by other whole numbers. In mathematics, these multiples play a crucial role in understanding number patterns and relationships. Each multiple of 26 is both a product of 26 and an integer divisor of larger numbers. Factors of 26 itself are 1, 2, 13, and 26, and its multiples are obtained through their multiplication with other integers. Recognizing these multiples helps in solving various mathematical problems related to division, factors, and common multiples.

## What are Multiples of 26?

Multiples of 26 are numbers obtained by multiplying 26 by any integer. These include 26, 52, 78, 104, 130, and so on. In general, a multiple of 26 is in the form 26n, where n is an integer.

Prime factorization of 26: 26 = 2 × 13 First 10 multiples of 26: 26, 52, 78, 104, 130, 156, 182, 208, 234, 260.

## For example, 78, 130, 156 and 234 are all multiples of 26, 265 is not a multiple of 26 for the following reasons:

Here’s the table format with the remainder last:

Table of 26

## Important Notes

### 1. Definition of Multiples

• Multiples of a number are the results you get when you multiply that number by an integer.
• Example: The multiples of 26 are 26, 52, 78, 104, etc.

### 2. Generating Multiples

• To generate the multiples of 26, simply multiply 26 by positive integers.
• Formula: 26×n26 \times n26×n where nnn is an integer (1, 2, 3,…).

### 3. Sequence Pattern

• The sequence of multiples of 26 forms an arithmetic sequence where each term increases by 26.
• Example: 26, 52, 78, 104, 130, 156, 182, 208, 234, 260.

### 4. Properties of Multiples

• Divisibility: Any multiple of 26 is also divisible by 2 and 13 since 26 = 2×13.
• Even Numbers: All multiples of 26 are even because 26 itself is an even number.

### 5. Applications in Real Life

• Grouping and Batching: Multiples of 26 can be useful in situations where items are grouped in sets of 26.
• Common Multiples: Useful for finding common time intervals or measurements in various fields such as science, engineering, and economics.

## Examples on Multiples of 26

### Example 1: Finding Specific Multiples

Problem: Identify the 15th multiple of 26.
To find the 15th multiple of 26, multiply 26 by 15. 26×15 = 390

The 15th multiple of 26 is 390.

### Example 2: Common Multiples

Problem: Find the smallest common multiple of 26 and 13.
Since 13 is a factor of 26, the smallest common multiple is the larger number, which is 26.
The smallest common multiple of 26 and 13 is 26.

### Example 3: Divisibility Check

Problem: Determine if 104 is a multiple of 26.
To check if 104 is a multiple of 26, divide 104 by 26. 104÷26 = 4 Since the result is a whole number with no remainder, 104 is a multiple of 26.

Yes, 104 is a multiple of 26.

### Example 4: Application in Real-Life Situations

Problem: A factory packs 26 bottles in each box. How many bottles are there in 50 boxes?
To find the total number of bottles, multiply the number of boxes by the number of bottles per box. 26×50 = 1300.

There are 1300 bottles in 50 boxes.

### Example 5: Sequences

Problem: List the first 5 multiples of 26.
Calculate the first 5 multiples by multiplying 26 by 1, 2, 3, 4, and 5:

• 26×1 = 26
• 26×2 = 52
• 26×3 = 78
• 26×4 = 104
• 26×5 = 130

The first 5 multiples of 26 are 26, 52, 78, 104, and 130.

### Example 6: Finding Multiples within a Range

Problem: Identify all multiples of 26 between 100 and 300.
Start with the smallest multiple of 26 greater than or equal to 100, which is 104. Continue adding 26 until reaching the largest multiple less than or equal to 300:

• 26×4 = 104
• 26×5 = 130
• 26×6 = 156
• 26×7 = 182
• 26×8 = 208
• 26×9 = 234
• 26×10 = 260
• 26×11 = 286.

The multiples of 26 between 100 and 300 are 104, 130, 156, 182, 208, 234, 260, and 286.

## What is a multiple of 26?

A multiple of 26 is a number that can be expressed as 26 times an integer. Examples include 26, 52, 78, and 104.

## How do you find multiples of 26?

To find multiples of 26, multiply 26 by any integer (positive, negative, or zero). For example, 26 × 3 = 78 and 26 × (-2) = -52.

## Is 104 a multiple of 26?

Yes, 104 is a multiple of 26 because 104 ÷ 26 equals 4, which is an integer.

## Are all multiples of 26 even numbers?

Yes, all multiples of 26 are even numbers because 26 itself is an even number, and the product of an even number with any integer is always even.

## What is the smallest positive multiple of 26?

The smallest positive multiple of 26 is 26 itself (26 × 1).

## Are multiples of 26 also multiples of 2 and 13?

Yes, since 26 is the product of 2 and 13 (26 = 2 × 13), any multiple of 26 is also a multiple of both 2 and 13.

## Can a multiple of 26 be a decimal?

No, multiples of 26 are always integers. Multiplying 26 by any integer will always result in an integer.

## What is the 10th multiple of 26?

The 10th multiple of 26 is 260 (26 × 10).

## Is 0 a multiple of 26?

Yes, 0 is a multiple of every integer, including 26, because 26 × 0 = 0.

## How many multiples of 26 are there between 100 and 300?

There are 8 multiples of 26 between 100 and 300: 104, 130, 156, 182, 208, 234, 260, and 286.

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