# Multiples of 29

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

## Multiples of 29

Multiples of 29 are the products obtained when 29 is multiplied by different integers. In mathematics, these numbers result from the multiplication of 29 with whole numbers like 1, 2, 3, and so on. Each multiple of 29 can be expressed as 29n, where n is an integer. The multiples of a number share common divisors and factors with the original number, making them an essential concept in understanding number properties and relationships. By exploring the multiples of 29, we delve into the broader realm of integers, multiplication, and number theory.

## What are Multiples of 29?

Multiples of 29 are the numbers that can be expressed as 29n, where n is an integer. These include 29, 58, 87, and so on, incrementing by 29 each time. Essentially, they are the products obtained by multiplying 29 with whole numbers.

Prime Factorization of 29 := 2 × 2 × 7 First 10 multiples of 29: 29, 58, 87, 116, 145, 174, 203, 232, 261 290.

Table of 29

## Important Notes

### 1. Definition of Multiples

A multiple of a number is the product of that number and an integer. For 29, the multiples are obtained by multiplying 29 by whole numbers like 1, 2, 3, etc.

### 2. First 10 Multiples of 29

The first 10 multiples of 29 are:

• 29 × 1 = 29
• 29 × 2 = 58
• 29 × 3 = 87
• 29 × 4 = 116
• 29 × 5 = 145
• 29 × 6 = 174
• 29 × 7 = 203
• 29 × 8 = 232
• 29 × 9 = 261
• 29 × 10 = 290

### 3. Properties of Multiples of 29

Even and Odd: Since 29 is an odd number, its multiples alternate between odd and even.

Divisibility: A number is a multiple of 29 if it can be divided by 29 without leaving a remainder.

### 4. Applications

Multiples of 29 can be used in various mathematical problems, such as finding common multiples, solving least common multiple (LCM) problems, and in sequences and series.

### 5. General Formula

The n-th multiple of 29 can be calculated using the formula: 29n, where n is a positive integer. For example, to find the 20th multiple of 29, you would compute 29×20 = 580.

## Examples on Multiples of 29

### Example 1: Identifying Multiples

Problem: Determine if 348 is a multiple of 29.

Divide 348 by 29. 348÷29 = 12 Since the quotient is an integer and there is no remainder, 348 is a multiple of 29. Specifically, 348 = 29×12.

### Example 2: Finding Common Multiples

Problem: Find the least common multiple (LCM) of 29 and 58.

List the multiples of each number:

• Multiples of 29: 29, 58, 87, 116, 145, …
• Multiples of 58: 58, 116, 174, 232, …

Identify the common multiples:

• The first common multiple is 58.

Therefore, the LCM of 29 and 58 is 58.

### Example 3: Real-Life Application

Problem: A factory produces 29 items per batch. How many items will be produced after 7 batches?

Multiply the number of items per batch by the number of batches: 29×7 = 203. Thus, 203 items will be produced after 7 batches.

### Example 4: Solving for a Multiple

Problem: Find the 15th multiple of 29.

Use the formula for the n-th multiple: 29×15 = 435 So, the 15th multiple of 29 is 435.

### Example 5: Practical Use in Scheduling

Problem: A bus arrives at a stop every 29 minutes. If the first bus arrives at 8:00 AM, at what times will the next three buses arrive?

• First bus: 8:00 AM
• Second bus: 8:00 AM + 29 minutes = 8:29 AM
• Third bus: 8:29 AM + 29 minutes = 8:58 AM
• Fourth bus: 8:58 AM + 29 minutes = 9:27 AM

So, the next three buses will arrive at 8:29 AM, 8:58 AM, and 9:27 AM.

## What is a multiple of 29?

A multiple of 29 is any number that can be expressed as 29 multiplied by an integer. Examples include 29, 58, 87, and so on.

## How do you find the multiples of 29?

To find multiples of 29, multiply 29 by any whole number (integer). For example, 29 × 1 = 29, 29 × 2 = 58, 29 × 3 = 87, etc.

## Are all multiples of 29 odd numbers?

No, multiples of 29 can be either odd or even. For example, 29 (29 × 1) is odd, but 58 (29 × 2) is even.

## Is 145 a multiple of 29?

Yes, 145 is a multiple of 29 because 29 × 5 = 145.

## What is the smallest multiple of 29?

The smallest multiple of 29 is 29 itself (29 × 1).

## How many multiples of 29 are there between 100 and 300?

Between 100 and 300, the multiples of 29 are 116, 145, 174, 203, 232, 261, and 290. There are 7 multiples in this range.

## Can a negative number be a multiple of 29?

Yes, a negative number can be a multiple of 29. For example, -29, -58, and -87 are multiples of 29.

## Are 29 and 58 multiples of each other?

29 is a multiple of itself, but 58 is a multiple of 29, as 58 = 29 × 2.

## Is zero a multiple of 29?

Yes, zero is considered a multiple of every number, including 29, because 29 × 0 = 0.

## What are the first five positive multiples of 29?

The first five positive multiples of 29 are 29, 58, 87, 116, and 145.

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