## 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

**.**

## For example, 87, 174, 232 and 261 are all multiples of 29, 436 is not a multiple of 29 for the following reasons:

Number | Calculation | Reason | Remainder |
---|---|---|---|

87 | 87÷29 = 3 | 87 is a multiple of 29 because it divides evenly. | 0 |

174 | 174÷29 = 6 | 174 is a multiple of 29 because it divides evenly. | 0 |

232 | 232÷29 = 8 | 232 is a multiple of 29 because it divides evenly. | 0 |

261 | 261÷29 = 9 | 261 is a multiple of 29 because it divides evenly. | 0 |

436 | 436÷29 = 15 | 436 is not a multiple of 29 because it does not divide evenly. | 1 |

## List of First 100 Multiples of 29 with Remainders

Number | Reason | Remainder |
---|---|---|

29 | 29 is a multiple of 29 because 29 × 1 = 29 | 0 |

58 | 58 is a multiple of 29 because 29 × 2 = 58 | 0 |

87 | 87 is a multiple of 29 because 29 × 3 = 87 | 0 |

116 | 116 is a multiple of 29 because 29 × 4 = 116 | 0 |

145 | 145 is a multiple of 29 because 29 × 5 = 145 | 0 |

174 | 174 is a multiple of 29 because 29 × 6 = 174 | 0 |

203 | 203 is a multiple of 29 because 29 × 7 = 203 | 0 |

232 | 232 is a multiple of 29 because 29 × 8 = 232 | 0 |

261 | 261 is a multiple of 29 because 29 × 9 = 261 | 0 |

290 | 290 is a multiple of 29 because 29 × 10 = 290 | 0 |

319 | 319 is a multiple of 29 because 29 × 11 = 319 | 0 |

348 | 348 is a multiple of 29 because 29 × 12 = 348 | 0 |

377 | 377 is a multiple of 29 because 29 × 13 = 377 | 0 |

406 | 406 is a multiple of 29 because 29 × 14 = 406 | 0 |

435 | 435 is a multiple of 29 because 29 × 15 = 435 | 0 |

464 | 464 is a multiple of 29 because 29 × 16 = 464 | 0 |

493 | 493 is a multiple of 29 because 29 × 17 = 493 | 0 |

522 | 522 is a multiple of 29 because 29 × 18 = 522 | 0 |

551 | 551 is a multiple of 29 because 29 × 19 = 551 | 0 |

580 | 580 is a multiple of 29 because 29 × 20 = 580 | 0 |

609 | 609 is a multiple of 29 because 29 × 21 = 609 | 0 |

638 | 638 is a multiple of 29 because 29 × 22 = 638 | 0 |

667 | 667 is a multiple of 29 because 29 × 23 = 667 | 0 |

696 | 696 is a multiple of 29 because 29 × 24 = 696 | 0 |

725 | 725 is a multiple of 29 because 29 × 25 = 725 | 0 |

754 | 754 is a multiple of 29 because 29 × 26 = 754 | 0 |

783 | 783 is a multiple of 29 because 29 × 27 = 783 | 0 |

812 | 812 is a multiple of 29 because 29 × 28 = 812 | 0 |

841 | 841 is a multiple of 29 because 29 × 29 = 841 | 0 |

870 | 870 is a multiple of 29 because 29 × 30 = 870 | 0 |

899 | 899 is a multiple of 29 because 29 × 31 = 899 | 0 |

928 | 928 is a multiple of 29 because 29 × 32 = 928 | 0 |

957 | 957 is a multiple of 29 because 29 × 33 = 957 | 0 |

986 | 986 is a multiple of 29 because 29 × 34 = 986 | 0 |

1015 | 1015 is a multiple of 29 because 29 × 35 = 1015 | 0 |

1044 | 1044 is a multiple of 29 because 29 × 36 = 1044 | 0 |

1073 | 1073 is a multiple of 29 because 29 × 37 = 1073 | 0 |

1102 | 1102 is a multiple of 29 because 29 × 38 = 1102 | 0 |

1131 | 1131 is a multiple of 29 because 29 × 39 = 1131 | 0 |

1160 | 1160 is a multiple of 29 because 29 × 40 = 1160 | 0 |

1189 | 1189 is a multiple of 29 because 29 × 41 = 1189 | 0 |

1218 | 1218 is a multiple of 29 because 29 × 42 = 1218 | 0 |

1247 | 1247 is a multiple of 29 because 29 × 43 = 1247 | 0 |

1276 | 1276 is a multiple of 29 because 29 × 44 = 1276 | 0 |

1305 | 1305 is a multiple of 29 because 29 × 45 = 1305 | 0 |

1334 | 1334 is a multiple of 29 because 29 × 46 = 1334 | 0 |

1363 | 1363 is a multiple of 29 because 29 × 47 = 1363 | 0 |

1392 | 1392 is a multiple of 29 because 29 × 48 = 1392 | 0 |

1421 | 1421 is a multiple of 29 because 29 × 49 = 1421 | 0 |

1450 | 1450 is a multiple of 29 because 29 × 50 = 1450 | 0 |

1479 | 1479 is a multiple of 29 because 29 × 51 = 1479 | 0 |

1508 | 1508 is a multiple of 29 because 29 × 52 = 1508 | 0 |

1537 | 1537 is a multiple of 29 because 29 × 53 = 1537 | 0 |

1566 | 1566 is a multiple of 29 because 29 × 54 = 1566 | 0 |

1595 | 1595 is a multiple of 29 because 29 × 55 = 1595 | 0 |

1624 | 1624 is a multiple of 29 because 29 × 56 = 1624 | 0 |

1653 | 1653 is a multiple of 29 because 29 × 57 = 1653 | 0 |

1682 | 1682 is a multiple of 29 because 29 × 58 = 1682 | 0 |

1711 | 1711 is a multiple of 29 because 29 × 59 = 1711 | 0 |

1740 | 1740 is a multiple of 29 because 29 × 60 = 1740 | 0 |

1769 | 1769 is a multiple of 29 because 29 × 61 = 1769 | 0 |

1798 | 1798 is a multiple of 29 because 29 × 62 = 1798 | 0 |

1827 | 1827 is a multiple of 29 because 29 × 63 = 1827 | 0 |

1856 | 1856 is a multiple of 29 because 29 × 64 = 1856 | 0 |

1885 | 1885 is a multiple of 29 because 29 × 65 = 1885 | 0 |

1914 | 1914 is a multiple of 29 because 29 × 66 = 1914 | 0 |

1943 | 1943 is a multiple of 29 because 29 × 67 = 1943 | 0 |

1972 | 1972 is a multiple of 29 because 29 × 68 = 1972 | 0 |

2001 | 2001 is a multiple of 29 because 29 × 69 = 2001 | 0 |

2030 | 2030 is a multiple of 29 because 29 × 70 = 2030 | 0 |

2059 | 2059 is a multiple of 29 because 29 × 71 = 2059 | 0 |

2088 | 2088 is a multiple of 29 because 29 × 72 = 2088 | 0 |

2117 | 2117 is a multiple of 29 because 29 × 73 = 2117 | 0 |

2146 | 2146 is a multiple of 29 because 29 × 74 = 2146 | 0 |

2175 | 2175 is a multiple of 29 because 29 × 75 = 2175 | 0 |

2204 | 2204 is a multiple of 29 because 29 × 76 = 2204 | 0 |

2233 | 2233 is a multiple of 29 because 29 × 77 = 2233 | 0 |

2262 | 2262 is a multiple of 29 because 29 × 78 = 2262 | 0 |

2291 | 2291 is a multiple of 29 because 29 × 79 = 2291 | 0 |

2320 | 2320 is a multiple of 29 because 29 × 80 = 2320 | 0 |

2349 | 2349 is a multiple of 29 because 29 × 81 = 2349 | 0 |

2378 | 2378 is a multiple of 29 because 29 × 82 = 2378 | 0 |

2407 | 2407 is a multiple of 29 because 29 × 83 = 2407 | 0 |

2436 | 2436 is a multiple of 29 because 29 × 84 = 2436 | 0 |

2465 | 2465 is a multiple of 29 because 29 × 85 = 2465 | 0 |

2494 | 2494 is a multiple of 29 because 29 × 86 = 2494 | 0 |

2523 | 2523 is a multiple of 29 because 29 × 87 = 2523 | 0 |

2552 | 2552 is a multiple of 29 because 29 × 88 = 2552 | 0 |

2581 | 2581 is a multiple of 29 because 29 × 89 = 2581 | 0 |

2610 | 2610 is a multiple of 29 because 29 × 90 = 2610 | 0 |

2639 | 2639 is a multiple of 29 because 29 × 91 = 2639 | 0 |

2668 | 2668 is a multiple of 29 because 29 × 92 = 2668 | 0 |

2697 | 2697 is a multiple of 29 because 29 × 93 = 2697 | 0 |

2726 | 2726 is a multiple of 29 because 29 × 94 = 2726 | 0 |

2755 | 2755 is a multiple of 29 because 29 × 95 = 2755 | 0 |

2784 | 2784 is a multiple of 29 because 29 × 96 = 2784 | 0 |

2813 | 2813 is a multiple of 29 because 29 × 97 = 2813 | 0 |

2842 | 2842 is a multiple of 29 because 29 × 98 = 2842 | 0 |

2871 | 2871 is a multiple of 29 because 29 × 99 = 2871 | 0 |

2900 | 2900 is a multiple of 29 because 29 × 100 = 2900 | 0 |

## Read More About Multiples 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.

## FAQs

## 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.