## Multiples of 83

Multiples of 83 are numbers that can be expressed as 83 × n, where n is an integer. These multiples follow a pattern, increasing by 83 each time (e.g., 83, 166, 249, 332, 415). Multiples of 83 are crucial in mathematics, particularly in algebraic concepts, squares, square roots, and fractions. They play a fundamental role in understanding number properties and performing various arithmetic operations efficiently. Recognizing these multiples aids in grasping more complex mathematical ideas and solving algebraic equations. Multiples of 83 serve as essential building blocks in number theory, helping to explore patterns, relationships, and the behavior of numbers within mathematical frameworks. Understanding multiples of 83 enhances mathematical proficiency and problem-solving skills.

## What are Multiples of 83?

**Multiples of 83 are numbers that can be expressed as 83×n, where n is an integer.** These numbers are always even and include values like 83, 166, 249, 332, and so on.

**Prime Factorization of 83 :** 1 × 83

**First 10 Multiples of 83 are 83, 166, 249, 332, 415, 498, 581, 664, 747, 830**

**First 50 Multiples of 83 are 83, 166, 249, 332, 415, 498, 581, 664, 747, 830, 913, 996, 1079, 1162, 1245, 1328, 1411, 1494, 1577, 1660, 1743, 1826, 1909, 1992, 2075, 2158, 2241, 2324, 2407, 2490, 2573, 2656, 2739, 2822, 2905, 2988, 3071, 3154, 3237, 3320, 3403, 3486, 3569, 3652, 3735, 3818, 3901, 3984, 4067, 4150, 4233, 4316, 4399, 4482, 4565, 4648, 4731, 4814, 4897, 4980, 5063, 5146, 5229, 5312, 5395, 5478, 5561, 5644, 5727, 5810, 5893, 5976, 6059, 6142, 6225, 6308, 6391, 6474, 6557, 6640, 6723, 6806, 6889, 6972, 7055, 7138, 7221, 7304, 7387, 7470, 7553, 7636, 7719, 7802, 7885, 7968, 8051, 8134, 8217, 8300, 8383.**

## For example, 83 , 80, 166 and 249 are all multiples of 83, 149 is not a multiple of 83 for the following reasons:

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

83 | 83 × 1 = 83, which is exactly divisible by 83 | 0 |

166 | 83 × 2 = 166, which is exactly divisible by 83 | 0 |

249 | 83 × 3 = 249, which is exactly divisible by 83 | 0 |

332 | 83 × 4 = 332, which is exactly divisible by 83 | 0 |

149 | 149 ÷ 83 is not an integer; not divisible by 83 | 66 |

## List of First 100 Multiples of 83 with Remainders

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

83 | 83 × 1 = 83, which is exactly divisible by 83 | 0 |

166 | 83 × 2 = 166, which is exactly divisible by 83 | 0 |

249 | 83 × 3 = 249, which is exactly divisible by 83 | 0 |

332 | 83 × 4 = 332, which is exactly divisible by 83 | 0 |

415 | 83 × 5 = 415, which is exactly divisible by 83 | 0 |

498 | 83 × 6 = 498, which is exactly divisible by 83 | 0 |

581 | 83 × 7 = 581, which is exactly divisible by 83 | 0 |

664 | 83 × 8 = 664, which is exactly divisible by 83 | 0 |

747 | 83 × 9 = 747, which is exactly divisible by 83 | 0 |

830 | 83 × 10 = 830, which is exactly divisible by 83 | 0 |

913 | 83 × 11 = 913, which is exactly divisible by 83 | 0 |

996 | 83 × 12 = 996, which is exactly divisible by 83 | 0 |

1079 | 83 × 13 = 1079, which is exactly divisible by 83 | 0 |

1162 | 83 × 14 = 1162, which is exactly divisible by 83 | 0 |

1245 | 83 × 15 = 1245, which is exactly divisible by 83 | 0 |

1328 | 83 × 16 = 1328, which is exactly divisible by 83 | 0 |

1411 | 83 × 17 = 1411, which is exactly divisible by 83 | 0 |

1494 | 83 × 18 = 1494, which is exactly divisible by 83 | 0 |

1577 | 83 × 19 = 1577, which is exactly divisible by 83 | 0 |

1660 | 83 × 20 = 1660, which is exactly divisible by 83 | 0 |

1743 | 83 × 21 = 1743, which is exactly divisible by 83 | 0 |

1826 | 83 × 22 = 1826, which is exactly divisible by 83 | 0 |

1909 | 83 × 23 = 1909, which is exactly divisible by 83 | 0 |

1992 | 83 × 24 = 1992, which is exactly divisible by 83 | 0 |

2075 | 83 × 25 = 2075, which is exactly divisible by 83 | 0 |

2158 | 83 × 26 = 2158, which is exactly divisible by 83 | 0 |

2241 | 83 × 27 = 2241, which is exactly divisible by 83 | 0 |

2324 | 83 × 28 = 2324, which is exactly divisible by 83 | 0 |

2407 | 83 × 29 = 2407, which is exactly divisible by 83 | 0 |

2490 | 83 × 30 = 2490, which is exactly divisible by 83 | 0 |

2573 | 83 × 31 = 2573, which is exactly divisible by 83 | 0 |

2656 | 83 × 32 = 2656, which is exactly divisible by 83 | 0 |

2739 | 83 × 33 = 2739, which is exactly divisible by 83 | 0 |

2822 | 83 × 34 = 2822, which is exactly divisible by 83 | 0 |

2905 | 83 × 35 = 2905, which is exactly divisible by 83 | 0 |

2988 | 83 × 36 = 2988, which is exactly divisible by 83 | 0 |

3071 | 83 × 37 = 3071, which is exactly divisible by 83 | 0 |

3154 | 83 × 38 = 3154, which is exactly divisible by 83 | 0 |

3237 | 83 × 39 = 3237, which is exactly divisible by 83 | 0 |

3320 | 83 × 40 = 3320, which is exactly divisible by 83 | 0 |

3403 | 83 × 41 = 3403, which is exactly divisible by 83 | 0 |

3486 | 83 × 42 = 3486, which is exactly divisible by 83 | 0 |

3569 | 83 × 43 = 3569, which is exactly divisible by 83 | 0 |

3652 | 83 × 44 = 3652, which is exactly divisible by 83 | 0 |

3735 | 83 × 45 = 3735, which is exactly divisible by 83 | 0 |

3818 | 83 × 46 = 3818, which is exactly divisible by 83 | 0 |

3901 | 83 × 47 = 3901, which is exactly divisible by 83 | 0 |

3984 | 83 × 48 = 3984, which is exactly divisible by 83 | 0 |

4067 | 83 × 49 = 4067, which is exactly divisible by 83 | 0 |

4150 | 83 × 50 = 4150, which is exactly divisible by 83 | 0 |

4233 | 83 × 51 = 4233, which is exactly divisible by 83 | 0 |

4316 | 83 × 52 = 4316, which is exactly divisible by 83 | 0 |

4399 | 83 × 53 = 4399, which is exactly divisible by 83 | 0 |

4482 | 83 × 54 = 4482, which is exactly divisible by 83 | 0 |

4565 | 83 × 55 = 4565, which is exactly divisible by 83 | 0 |

4648 | 83 × 56 = 4648, which is exactly divisible by 83 | 0 |

4731 | 83 × 57 = 4731, which is exactly divisible by 83 | 0 |

4814 | 83 × 58 = 4814, which is exactly divisible by 83 | 0 |

4897 | 83 × 59 = 4897, which is exactly divisible by 83 | 0 |

4980 | 83 × 60 = 4980, which is exactly divisible by 83 | 0 |

5063 | 83 × 61 = 5063, which is exactly divisible by 83 | 0 |

5146 | 83 × 62 = 5146, which is exactly divisible by 83 | 0 |

5229 | 83 × 63 = 5229, which is exactly divisible by 83 | 0 |

5312 | 83 × 64 = 5312, which is exactly divisible by 83 | 0 |

5395 | 83 × 65 = 5395, which is exactly divisible by 83 | 0 |

5478 | 83 × 66 = 5478, which is exactly divisible by 83 | 0 |

5561 | 83 × 67 = 5561, which is exactly divisible by 83 | 0 |

5644 | 83 × 68 = 5644, which is exactly divisible by 83 | 0 |

5727 | 83 × 69 = 5727, which is exactly divisible by 83 | 0 |

5810 | 83 × 70 = 5810, which is exactly divisible by 83 | 0 |

5893 | 83 × 71 = 5893, which is exactly divisible by 83 | 0 |

5976 | 83 × 72 = 5976, which is exactly divisible by 83 | 0 |

6059 | 83 × 73 = 6059, which is exactly divisible by 83 | 0 |

6142 | 83 × 74 = 6142, which is exactly divisible by 83 | 0 |

6225 | 83 × 75 = 6225, which is exactly divisible by 83 | 0 |

6308 | 83 × 76 = 6308, which is exactly divisible by 83 | 0 |

6391 | 83 × 77 = 6391, which is exactly divisible by 83 | 0 |

6474 | 83 × 78 = 6474, which is exactly divisible by 83 | 0 |

6557 | 83 × 79 = 6557, which is exactly divisible by 83 | 0 |

6640 | 83 × 80 = 6640, which is exactly divisible by 83 | 0 |

6723 | 83 × 81 = 6723, which is exactly divisible by 83 | 0 |

6806 | 83 × 82 = 6806, which is exactly divisible by 83 | 0 |

6889 | 83 × 83 = 6889, which is exactly divisible by 83 | 0 |

6972 | 83 × 84 = 6972, which is exactly divisible by 83 | 0 |

7055 | 83 × 85 = 7055, which is exactly divisible by 83 | 0 |

7138 | 83 × 86 = 7138, which is exactly divisible by 83 | 0 |

7221 | 83 × 87 = 7221, which is exactly divisible by 83 | 0 |

7304 | 83 × 88 = 7304, which is exactly divisible by 83 | 0 |

7387 | 83 × 89 = 7387, which is exactly divisible by 83 | 0 |

7470 | 83 × 90 = 7470, which is exactly divisible by 83 | 0 |

7553 | 83 × 91 = 7553, which is exactly divisible by 83 | 0 |

7636 | 83 × 92 = 7636, which is exactly divisible by 83 | 0 |

7719 | 83 × 93 = 7719, which is exactly divisible by 83 | 0 |

7802 | 83 × 94 = 7802, which is exactly divisible by 83 | 0 |

7885 | 83 × 95 = 7885, which is exactly divisible by 83 | 0 |

7968 | 83 × 96 = 7968, which is exactly divisible by 83 | 0 |

8051 | 83 × 97 = 8051, which is exactly divisible by 83 | 0 |

8134 | 83 × 98 = 8134, which is exactly divisible by 83 | 0 |

8217 | 83 × 99 = 8217, which is exactly divisible by 83 | 0 |

8300 | 83 × 100 = 8300, which is exactly divisible by 83 | 0 |

## Read More About Multiples of 83

## Important Notes

**Odd Numbers:**All multiples of 83 are odd numbers, meaning they end in 1, 3, 5, 7, or 9.**Divisibility:**A number is a multiple of 83 if it can be divided by 83 with no remainder.**Factors:**Multiples of 83 have 83 as one of their factors.**Infinite Sequence:**There are infinitely many multiples of 83, extending indefinitely as 83, 166, 249, 332, 415, and so on.**Arithmetic Pattern:**The difference between consecutive multiples of 83 is always 83.

## Examples on Multiples of 83

#### Simple Multiples

83: 83×1 = 83

166: 83×2 = 166

249: 83×3 = 249

#### Larger Multiples

830: 83×10 = 830

1660: 83×20 = 1660

3320: 83×40 = 3320

## Real-Life Examples

**Time:**83 minutes is a multiple of 83 because 83×1=83.**Money:**$83 is a multiple of 83 because 83×1=83.**Measurements:**249 inches (20.75 feet) is a multiple of 83 because 83×3=249.

## Practical Examples of Multiples of 83

**Classroom Seating:**A school arranges chairs in rows of 83, so if there are 166 or 249 chairs, they are multiples of 83.**Event Planning:**An event coordinator sets up tables with 83 seats each. Thus, 83, 166, or 249 guests can be seated in multiples of 83.**Shipping:**A warehouse packs boxes in batches of 83, ensuring shipments of 83, 166, or 249 items are multiples of 83.**Construction:**A builder uses 83 bricks per section of a wall, so sections requiring 83, 166, or 249 bricks are in multiples of 83.**Inventory Management:**A store orders supplies in multiples of 83, maintaining stock levels with 83, 166, or 249 items.

## Practical Applications

**Counting by Eighty-Threes:** When counting by eighty-threes (83, 166, 249, 332…), you are listing the multiples of 83.

**Odd Numbers:** Any number that is a multiple of 83, such as 166 or 249, is a multiple of 83 because it can be divided evenly by 83.

**Is 249 a multiple of 83?**

Yes, 249 is a multiple of 83 because 83×3=249.

**What are the first five multiples of 83?**

The first five multiples of 83 are 83, 166, 249, 332, and 415.

**Is 83 a common multiple of any other number?**

Yes, 83 is a common multiple of 1, 83.

**How can multiples of 83 be used in real life?**

Multiples of 83 can be used in scenarios involving grouping, packaging, or arranging items in sets of 83.

**What is the largest multiple of 83 less than 1000?**

The largest multiple of 83 less than 1000 is 913 (83×11=913).

**Are multiples of 83 used in mathematics?**

Yes, multiples of 83 are used in various mathematical concepts, including algebra and number theory.

**Is 900 a multiple of 83?**

No, 900 is not a multiple of 83 because 900÷83 does not result in an integer.

**Can multiples of 83 be negative?**

Yes, multiples of 83 can be negative if multiplied by a negative integer (e.g., 83×-1=-83).

**Is 747 a multiple of 83?**

Yes, 747 is a multiple of 83 because 83×9=747.

**Can a number be both a multiple of 83 and another number?**

**Can a number be both a multiple of 83 and another number?**

Yes, a number can be a multiple of 83 and another number if both numbers share common factors. For example, 166 is a multiple of 83 and 2.

**What is the smallest multiple of 83?**

The smallest multiple of 83 is 83 itself.