# Multiples of 23

Created by: Team Maths - Examples.com, Last Updated: May 23, 2024

## Multiples of 23

Multiples of 23 are numbers obtained by multiplying 23 by any integer. In mathematics, a multiple is a product of a number and an integer. The sequence of multiples of 23 includes 23, 46, 69, and so on. These numbers are significant in number theory as they illustrate the relationship between multiplication, factors, and divisors. Understanding multiples helps in identifying common factors and solving problems related to divisibility and integer operations.

## What are Multiples of 23?

Multiples of 23 are the products obtained when 23 is multiplied by integers (e.g., 23, 46, 69, 92). They form an arithmetic sequence where each term increases by 23. These multiples are essential in understanding factors, divisors, and various mathematical operations involving integers.

Prime factorization of 23: 23 = 1 × 23 First 10 multiples of 23: 23, 46, 69, 92, 115, 138, 161, 184, 207, 230.

Table of 23

## Important Notes

• Definition: A multiple of 23 is any number that can be expressed as 23×n, where n is an integer.
• Sequence: The sequence of multiples of 23 starts at 23 and increases by 23 each time: 23, 46, 69, 92, 115, etc.
• Divisibility: For a number to be a multiple of 23, it must be divisible by 23 without leaving a remainder.
• Prime Number: Since 23 is a prime number, its only factors are 1 and 23.
• Applications: Understanding multiples of 23 is useful in number theory, arithmetic operations, and finding common multiples in problems involving division and multiplication.

## Examples on Multiples of 23

### Example 1: Calculating the 5th Multiple of 23

• Step 1: Identify the position of the multiple.
• Step 2: Multiply 23 by 5.23×5 = 115
• Result: The 5th multiple of 23 is 115.

### Example 2: Checking if 184 is a Multiple of 23

• Step 1: Divide 184 by 23.184÷23 = 8
• Step 2: Check if the quotient is an integer without a remainder.
• Result: Since the quotient is 8 (an integer), 184 is a multiple of 23.

### Example 3: Finding the Next Multiple of 23 After 69

• Step 1: Identify the last known multiple (69).
• Step 2: Add 23 to the last multiple.69+23 = 92
• Result: The next multiple of 23 after 69 is 92.

### Example 4: Determining if 250 is a Multiple of 23

• Step 1: Divide 250 by 23.250÷23 = 10.87
• Step 2: Check the remainder.250÷23 = 10
• Result: Since the quotient is not an integer and there is a remainder of 20, 250 is not a multiple of 23.

### Example 5: Calculating the 12th Multiple of 23

• Step 1: Identify the position of the multiple.
• Step 2: Multiply 23 by 12.23×12 = 276
• Result: The 12th multiple of 23 is 276.

## What are multiples of 23?

Multiples of 23 are numbers that can be expressed as 23×n, where n is an integer. Examples include 23, 46, 69, 92, and so on.

## How do you find multiples of 23?

To find multiples of 23, multiply 23 by any integer. For example, 23×2 = 46 and 23×3 = 69.

## Is 46 a multiple of 23?

Yes, 46 is a multiple of 23 because 23×2 = 46.

## How can you verify if a number is a multiple of 23?

To verify if a number is a multiple of 23, divide the number by 23. If the quotient is an integer and there is no remainder, it is a multiple of 23.

## Are multiples of 23 always even?

No, multiples of 23 are not always even. For example, 23 itself is an odd number.

## What is the 10th multiple of 23?

The 10th multiple of 23 is 23×10 = 230.

## Is 115 a multiple of 23?

Yes, 115 is a multiple of 23 because 23×5 = 115.

## What is the next multiple of 23 after 138?

The next multiple of 23 after 138 is 138+23 = 161.

## Why is 69 considered a multiple of 23?

69 is considered a multiple of 23 because 23×3 = 69.

## Can a negative number be a multiple of 23?

Yes, negative numbers can be multiples of 23. For example, -23 and -46 are multiples of 23 because 23×−1 = −23 and 23×−2 = −46.

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