## Multiples of 27

Multiples of 27 are integers obtained by multiplying 27 by any whole number. In mathematics, multiples are numbers that result from multiplying a given number by the set of integers. The number 27 itself is both a factor and a divisor of its multiples. Understanding multiples helps in grasping key concepts like factors, divisors, and multiplication. This knowledge is essential for various mathematical operations and problem-solving.

## What are Multiples of 27?

**Multiples of 27 are numbers that can be expressed as 27 times an integer.** These numbers follow the sequence 27, 54, 81, 108, and so on. Each multiple results from multiplying 27 by whole numbers: 1, 2, 3, 4, etc.

**Prime factorization of 27**: 27 = 3 × 3 × 3 = 3³

**First 10 multiples of 27**: 27, 54, 81, 108, 135, 162, 189, 216, 243 270.

## For example, 81, 135, 189 and 243 are all multiples of 27, 352 is not a multiple of 27 for the following reasons:

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

81 | 81÷27 = 3 | 81 is a multiple of 27 because it divides evenly. | 0 |

135 | 135÷27 = 5 | 135 is a multiple of 27 because it divides evenly. | 0 |

189 | 189÷27 = 7 | 189 is a multiple of 27 because it divides evenly. | 0 |

243 | 243÷27 = 9 | 243 is a multiple of 27 because it divides evenly. | 0 |

352 | 352÷27 = 13 | 352 is not a multiple of 27 because it does not divide evenly. | 1 |

## List of First 100 Multiples of 27 with Remainders

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

27 | 27 is a multiple of 27 because 27 × 1 = 27 | 0 |

54 | 54 is a multiple of 27 because 27 × 2 = 54 | 0 |

81 | 81 is a multiple of 27 because 27 × 3 = 81 | 0 |

108 | 108 is a multiple of 27 because 27 × 4 = 108 | 0 |

135 | 135 is a multiple of 27 because 27 × 5 = 135 | 0 |

162 | 162 is a multiple of 27 because 27 × 6 = 162 | 0 |

189 | 189 is a multiple of 27 because 27 × 7 = 189 | 0 |

216 | 216 is a multiple of 27 because 27 × 8 = 216 | 0 |

243 | 243 is a multiple of 27 because 27 × 9 = 243 | 0 |

270 | 270 is a multiple of 27 because 27 × 10 = 270 | 0 |

297 | 297 is a multiple of 27 because 27 × 11 = 297 | 0 |

324 | 324 is a multiple of 27 because 27 × 12 = 324 | 0 |

351 | 351 is a multiple of 27 because 27 × 13 = 351 | 0 |

378 | 378 is a multiple of 27 because 27 × 14 = 378 | 0 |

405 | 405 is a multiple of 27 because 27 × 15 = 405 | 0 |

432 | 432 is a multiple of 27 because 27 × 16 = 432 | 0 |

459 | 459 is a multiple of 27 because 27 × 17 = 459 | 0 |

486 | 486 is a multiple of 27 because 27 × 18 = 486 | 0 |

513 | 513 is a multiple of 27 because 27 × 19 = 513 | 0 |

540 | 540 is a multiple of 27 because 27 × 20 = 540 | 0 |

567 | 567 is a multiple of 27 because 27 × 21 = 567 | 0 |

594 | 594 is a multiple of 27 because 27 × 22 = 594 | 0 |

621 | 621 is a multiple of 27 because 27 × 23 = 621 | 0 |

648 | 648 is a multiple of 27 because 27 × 24 = 648 | 0 |

675 | 675 is a multiple of 27 because 27 × 25 = 675 | 0 |

702 | 702 is a multiple of 27 because 27 × 26 = 702 | 0 |

729 | 729 is a multiple of 27 because 27 × 27 = 729 | 0 |

756 | 756 is a multiple of 27 because 27 × 28 = 756 | 0 |

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

810 | 810 is a multiple of 27 because 27 × 30 = 810 | 0 |

837 | 837 is a multiple of 27 because 27 × 31 = 837 | 0 |

864 | 864 is a multiple of 27 because 27 × 32 = 864 | 0 |

891 | 891 is a multiple of 27 because 27 × 33 = 891 | 0 |

918 | 918 is a multiple of 27 because 27 × 34 = 918 | 0 |

945 | 945 is a multiple of 27 because 27 × 35 = 945 | 0 |

972 | 972 is a multiple of 27 because 27 × 36 = 972 | 0 |

999 | 999 is a multiple of 27 because 27 × 37 = 999 | 0 |

1026 | 1026 is a multiple of 27 because 27 × 38 = 1026 | 0 |

1053 | 1053 is a multiple of 27 because 27 × 39 = 1053 | 0 |

1080 | 1080 is a multiple of 27 because 27 × 40 = 1080 | 0 |

1107 | 1107 is a multiple of 27 because 27 × 41 = 1107 | 0 |

1134 | 1134 is a multiple of 27 because 27 × 42 = 1134 | 0 |

1161 | 1161 is a multiple of 27 because 27 × 43 = 1161 | 0 |

1188 | 1188 is a multiple of 27 because 27 × 44 = 1188 | 0 |

1215 | 1215 is a multiple of 27 because 27 × 45 = 1215 | 0 |

1242 | 1242 is a multiple of 27 because 27 × 46 = 1242 | 0 |

1269 | 1269 is a multiple of 27 because 27 × 47 = 1269 | 0 |

1296 | 1296 is a multiple of 27 because 27 × 48 = 1296 | 0 |

1323 | 1323 is a multiple of 27 because 27 × 49 = 1323 | 0 |

1350 | 1350 is a multiple of 27 because 27 × 50 = 1350 | 0 |

1377 | 1377 is a multiple of 27 because 27 × 51 = 1377 | 0 |

1404 | 1404 is a multiple of 27 because 27 × 52 = 1404 | 0 |

1431 | 1431 is a multiple of 27 because 27 × 53 = 1431 | 0 |

1458 | 1458 is a multiple of 27 because 27 × 54 = 1458 | 0 |

1485 | 1485 is a multiple of 27 because 27 × 55 = 1485 | 0 |

1512 | 1512 is a multiple of 27 because 27 × 56 = 1512 | 0 |

1539 | 1539 is a multiple of 27 because 27 × 57 = 1539 | 0 |

1566 | 1566 is a multiple of 27 because 27 × 58 = 1566 | 0 |

1593 | 1593 is a multiple of 27 because 27 × 59 = 1593 | 0 |

1620 | 1620 is a multiple of 27 because 27 × 60 = 1620 | 0 |

1647 | 1647 is a multiple of 27 because 27 × 61 = 1647 | 0 |

1674 | 1674 is a multiple of 27 because 27 × 62 = 1674 | 0 |

1701 | 1701 is a multiple of 27 because 27 × 63 = 1701 | 0 |

1728 | 1728 is a multiple of 27 because 27 × 64 = 1728 | 0 |

1755 | 1755 is a multiple of 27 because 27 × 65 = 1755 | 0 |

1782 | 1782 is a multiple of 27 because 27 × 66 = 1782 | 0 |

1809 | 1809 is a multiple of 27 because 27 × 67 = 1809 | 0 |

1836 | 1836 is a multiple of 27 because 27 × 68 = 1836 | 0 |

1863 | 1863 is a multiple of 27 because 27 × 69 = 1863 | 0 |

1890 | 1890 is a multiple of 27 because 27 × 70 = 1890 | 0 |

1917 | 1917 is a multiple of 27 because 27 × 71 = 1917 | 0 |

1944 | 1944 is a multiple of 27 because 27 × 72 = 1944 | 0 |

1971 | 1971 is a multiple of 27 because 27 × 73 = 1971 | 0 |

1998 | 1998 is a multiple of 27 because 27 × 74 = 1998 | 0 |

2025 | 2025 is a multiple of 27 because 27 × 75 = 2025 | 0 |

2052 | 2052 is a multiple of 27 because 27 × 76 = 2052 | 0 |

2079 | 2079 is a multiple of 27 because 27 × 77 = 2079 | 0 |

2106 | 2106 is a multiple of 27 because 27 × 78 = 2106 | 0 |

2133 | 2133 is a multiple of 27 because 27 × 79 = 2133 | 0 |

2160 | 2160 is a multiple of 27 because 27 × 80 = 2160 | 0 |

2187 | 2187 is a multiple of 27 because 27 × 81 = 2187 | 0 |

2214 | 2214 is a multiple of 27 because 27 × 82 = 2214 | 0 |

2241 | 2241 is a multiple of 27 because 27 × 83 = 2241 | 0 |

2268 | 2268 is a multiple of 27 because 27 × 84 = 2268 | 0 |

2295 | 2295 is a multiple of 27 because 27 × 85 = 2295 | 0 |

2322 | 2322 is a multiple of 27 because 27 × 86 = 2322 | 0 |

2349 | 2349 is a multiple of 27 because 27 × 87 = 2349 | 0 |

2376 | 2376 is a multiple of 27 because 27 × 88 = 2376 | 0 |

2403 | 2403 is a multiple of 27 because 27 × 89 = 2403 | 0 |

2430 | 2430 is a multiple of 27 because 27 × 90 = 2430 | 0 |

2457 | 2457 is a multiple of 27 because 27 × 91 = 2457 | 0 |

2484 | 2484 is a multiple of 27 because 27 × 92 = 2484 | 0 |

2511 | 2511 is a multiple of 27 because 27 × 93 = 2511 | 0 |

2538 | 2538 is a multiple of 27 because 27 × 94 = 2538 | 0 |

2565 | 2565 is a multiple of 27 because 27 × 95 = 2565 | 0 |

2592 | 2592 is a multiple of 27 because 27 × 96 = 2592 | 0 |

2619 | 2619 is a multiple of 27 because 27 × 97 = 2619 | 0 |

2646 | 2646 is a multiple of 27 because 27 × 98 = 2646 | 0 |

2673 | 2673 is a multiple of 27 because 27 × 99 = 2673 | 0 |

2700 | 2700 is a multiple of 27 because 27 × 100 = 2700 | 0 |

## Read More About Multiples of 27

## Important Notes

### Definition

**Multiples of 27**are numbers that can be expressed as 27 times an integer.- The sequence starts from 27 and increases by 27 each time (i.e., 27, 54, 81, 108, etc.).

### 2. Pattern and Sequence

- The sequence of multiples of 27 is
**arithmetic**, with a common difference of 27. - Formula to find the n-th multiple: 27n where n is a positive integer.

### 3. First 10 Multiples

- The first 10 multiples of 27 are: 27, 54, 81, 108, 135, 162, 189, 216, 243, 270.

### 4. Properties

- All multiples of 27 are
**divisible by 27**. - They are also multiples of 3 and 9, as 27 is a multiple of both.

### 5. Applications

**Common multiples**: When finding common multiples with another number, such as in least common multiple (LCM) calculations.**Real-life examples**: Situations involving grouping or partitioning into 27 parts, such as packaging or distributing items.

## Examples on Multiples of 27

### Example 1: Finding Multiples in a Range

**Problem:** Identify all multiples of 27 between 100 and 500.

Start with the smallest multiple of 27 greater than or equal to 100.

27×4 = 108

Continue finding subsequent multiples of 27 until reaching or exceeding 500.

- 27×5 = 135
- 27×6 = 162
- 27×7 = 189
- 27×8 = 216
- 27×9 = 243
- 27×10 = 270
- 27×11 = 297
- 27×12 = 324
- 27×13 = 351
- 27×14 = 378
- 27×15 = 405
- 27×16 = 432
- 27×17 = 459
- 27×18 = 486

**Multiples of 27 between 100 and 500:** 108, 135, 162, 189, 216, 243, 270, 297, 324, 351, 378, 405, 432, 459, 486.

### Example 2: Using Multiples to Solve a Word Problem

**Problem:** A factory produces 27 widgets per hour. How many widgets will the factory produce in an 8-hour workday?

Find the total number of widgets produced in 8 hours by multiplying 27 by 8.

27×8 = 216

The factory will produce 216 widgets in an 8-hour workday.

### Example 3: Determining Common Multiples

**Problem:** Find the least common multiple (LCM) of 27 and 36.

List the first few multiples of each number:

- Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, 270, …
- Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, …

Identify the smallest common multiple.

Common multiples: 108, 216, 324, …

The least common multiple (LCM) of 27 and 36 is 108.

### Example 4: Using Multiples for Divisibility

**Problem:** Determine if 405 is a multiple of 27.

Divide 405 by 27.

405÷27 = 15

Since 15 is an integer, 405 is a multiple of 27.

Yes, 405 is a multiple of 27.

### Example 5: Multiples in Sequences

**Problem:** Find the 12th multiple of 27.

Multiply 27 by 12.

27×12 = 324

The 12th multiple of 27 is 324.

## FAQs

## What are the first five multiples of 27?

The first five multiples of 27 are 27, 54, 81, 108, and 135.

## How do you determine if a number is a multiple of 27?

A number is a multiple of 27 if it can be divided by 27 without leaving a remainder.

## Is 270 a multiple of 27?

Yes, 270 is a multiple of 27 because 270 ÷ 27 = 10.

## What is the 10th multiple of 27?

The 10th multiple of 27 is 270 (27 × 10 = 270).

## Are multiples of 27 always odd?

No, multiples of 27 can be both odd and even. For example, 54 (27 × 2) is even, and 27 is odd.

## What is the least common multiple (LCM) of 27 and 36?

The least common multiple of 27 and 36 is 108.

## How many multiples of 27 are there between 100 and 200?

There are three multiples of 27 between 100 and 200: 108, 135, and 162.

## Can multiples of 27 be negative?

Yes, multiples of 27 can be negative. For example, -27, -54, and -81 are negative multiples of 27.

## What is the 15th multiple of 27?

The 15th multiple of 27 is 405 (27 × 15 = 405).

## Are all multiples of 27 also multiples of 3?

Yes, since 27 is a multiple of 3, all multiples of 27 are also multiples of 3.