## Multiples of 84

Multiples of 84 are numbers expressed as 84 × n, where n is an integer. These multiples increase by 84 each time (e.g., 84, 168, 252, 336, 420) and are not necessarily even. They are vital in mathematics, especially in algebra, squares, square roots, and fractions. Understanding multiples of 84 helps in performing arithmetic operations efficiently and in comprehending number properties. Recognizing these multiples is crucial for solving algebraic equations and grasping more complex mathematical concepts. They serve as fundamental building blocks in number theory, aiding in the exploration of patterns, relationships, and the behavior of numbers within mathematical frameworks. Multiples of 84 play a significant role in enhancing mathematical problem-solving skills.

## What are Multiples of 84?

**Multiples of 84 are numbers that can be expressed as 84×n, where n is an integer.** These numbers are always even and include values like 84, 168, 252, 336, and so on.

**Prime Factorization of 84 :** 2 × 2 × 3 × 7

**First 10 Multiples of 84 are 84, 168, 252, 336, 420, 504, 588, 672, 756, 840**

**First 50 Multiples of 84 are 84, 168, 252, 336, 420, 504, 588, 672, 756, 840, 924, 1008, 1092, 1176, 1260, 1344, 1428, 1512, 1596, 1680, 1764, 1848, 1932, 2016, 2100, 2184, 2268, 2352, 2436, 2520, 2604, 2688, 2772, 2856, 2940, 3024, 3108, 3192, 3276, 3360, 3444, 3528, 3612, 3696, 3780, 3864, 3948, 4032, 4116, 4200**

## For example, 84, 168, 252 and 336 are all multiples of 84, 132 is not a multiple of 84 for the following reasons:

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

84 | 84 × 1, which equals 84, making it a multiple of 84 | 0 |

168 | 84 × 2, which equals 168, making it a multiple of 84 | 0 |

252 | 84 × 3, which equals 252, making it a multiple of 84 | 0 |

336 | 84 × 4, which equals 336, making it a multiple of 84 | 0 |

132 | 132 ÷ 84 is not an integer, thus 132 is not a multiple of 84 | 48 |

## List of First 100 Multiples of 84 with Remainders

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

84 | 84 × 1, which equals 84 | 0 |

168 | 84 × 2, which equals 168 | 0 |

252 | 84 × 3, which equals 252 | 0 |

336 | 84 × 4, which equals 336 | 0 |

420 | 84 × 5, which equals 420 | 0 |

504 | 84 × 6, which equals 504 | 0 |

588 | 84 × 7, which equals 588 | 0 |

672 | 84 × 8, which equals 672 | 0 |

756 | 84 × 9, which equals 756 | 0 |

840 | 84 × 10, which equals 840 | 0 |

924 | 84 × 11, which equals 924 | 0 |

1008 | 84 × 12, which equals 1008 | 0 |

1092 | 84 × 13, which equals 1092 | 0 |

1176 | 84 × 14, which equals 1176 | 0 |

1260 | 84 × 15, which equals 1260 | 0 |

1344 | 84 × 16, which equals 1344 | 0 |

1428 | 84 × 17, which equals 1428 | 0 |

1512 | 84 × 18, which equals 1512 | 0 |

1596 | 84 × 19, which equals 1596 | 0 |

1680 | 84 × 20, which equals 1680 | 0 |

1764 | 84 × 21, which equals 1764 | 0 |

1848 | 84 × 22, which equals 1848 | 0 |

1932 | 84 × 23, which equals 1932 | 0 |

2016 | 84 × 24, which equals 2016 | 0 |

2100 | 84 × 25, which equals 2100 | 0 |

2184 | 84 × 26, which equals 2184 | 0 |

2268 | 84 × 27, which equals 2268 | 0 |

2352 | 84 × 28, which equals 2352 | 0 |

2436 | 84 × 29, which equals 2436 | 0 |

2520 | 84 × 30, which equals 2520 | 0 |

2604 | 84 × 31, which equals 2604 | 0 |

2688 | 84 × 32, which equals 2688 | 0 |

2772 | 84 × 33, which equals 2772 | 0 |

2856 | 84 × 34, which equals 2856 | 0 |

2940 | 84 × 35, which equals 2940 | 0 |

3024 | 84 × 36, which equals 3024 | 0 |

3108 | 84 × 37, which equals 3108 | 0 |

3192 | 84 × 38, which equals 3192 | 0 |

3276 | 84 × 39, which equals 3276 | 0 |

3360 | 84 × 40, which equals 3360 | 0 |

3444 | 84 × 41, which equals 3444 | 0 |

3528 | 84 × 42, which equals 3528 | 0 |

3612 | 84 × 43, which equals 3612 | 0 |

3696 | 84 × 44, which equals 3696 | 0 |

3780 | 84 × 45, which equals 3780 | 0 |

3864 | 84 × 46, which equals 3864 | 0 |

3948 | 84 × 47, which equals 3948 | 0 |

4032 | 84 × 48, which equals 4032 | 0 |

4116 | 84 × 49, which equals 4116 | 0 |

4200 | 84 × 50, which equals 4200 | 0 |

4284 | 84 × 51, which equals 4284 | 0 |

4368 | 84 × 52, which equals 4368 | 0 |

4452 | 84 × 53, which equals 4452 | 0 |

4536 | 84 × 54, which equals 4536 | 0 |

4620 | 84 × 55, which equals 4620 | 0 |

4704 | 84 × 56, which equals 4704 | 0 |

4788 | 84 × 57, which equals 4788 | 0 |

4872 | 84 × 58, which equals 4872 | 0 |

4956 | 84 × 59, which equals 4956 | 0 |

5040 | 84 × 60, which equals 5040 | 0 |

5124 | 84 × 61, which equals 5124 | 0 |

5208 | 84 × 62, which equals 5208 | 0 |

5292 | 84 × 63, which equals 5292 | 0 |

5376 | 84 × 64, which equals 5376 | 0 |

5460 | 84 × 65, which equals 5460 | 0 |

5544 | 84 × 66, which equals 5544 | 0 |

5628 | 84 × 67, which equals 5628 | 0 |

5712 | 84 × 68, which equals 5712 | 0 |

5796 | 84 × 69, which equals 5796 | 0 |

5880 | 84 × 70, which equals 5880 | 0 |

5964 | 84 × 71, which equals 5964 | 0 |

6048 | 84 × 72, which equals 6048 | 0 |

6132 | 84 × 73, which equals 6132 | 0 |

6216 | 84 × 74, which equals 6216 | 0 |

6300 | 84 × 75, which equals 6300 | 0 |

6384 | 84 × 76, which equals 6384 | 0 |

6468 | 84 × 77, which equals 6468 | 0 |

6552 | 84 × 78, which equals 6552 | 0 |

6636 | 84 × 79, which equals 6636 | 0 |

6720 | 84 × 80, which equals 6720 | 0 |

6804 | 84 × 81, which equals 6804 | 0 |

6888 | 84 × 82, which equals 6888 | 0 |

6972 | 84 × 83, which equals 6972 | 0 |

7056 | 84 × 84, which equals 7056 | 0 |

7140 | 84 × 85, which equals 7140 | 0 |

7224 | 84 × 86, which equals 7224 | 0 |

7308 | 84 × 87, which equals 7308 | 0 |

7392 | 84 × 88, which equals 7392 | 0 |

7476 | 84 × 89, which equals 7476 | 0 |

7560 | 84 × 90, which equals 7560 | 0 |

7644 | 84 × 91, which equals 7644 | 0 |

7728 | 84 × 92, which equals 7728 | 0 |

7812 | 84 × 93, which equals 7812 | 0 |

7896 | 84 × 94, which equals 7896 | 0 |

7980 | 84 × 95, which equals 7980 | 0 |

8064 | 84 × 96, which equals 8064 | 0 |

8148 | 84 × 97, which equals 8148 | 0 |

8232 | 84 × 98, which equals 8232 | 0 |

8316 | 84 × 99, which equals 8316 | 0 |

8400 | 84 × 100, which equals 8400 | 0 |

## Read More About Multiples of 84

## Important Notes

**Even Numbers**: All multiples of 84 are even numbers, meaning they end in 0, 2, 4, 6, or 8.**Divisibility****:**A number is a multiple of 84 if it can be divided by 84 with no remainder.**Factors****:**Multiples of 84 have 84 as one of their factors.**Infinite Sequence****:**There are infinitely many multiples of 84, extending indefinitely as 84, 168, 252, 336, 420, and so on.**Arithmetic Pattern****:**The difference between consecutive multiples of 84 is always 84.

## Examples on Multiples of 84

#### Simple Multiples

**84**: 84 × 1 = 84**168**: 84 × 2 = 168**252**: 84 × 3 = 252

#### Larger Multiples

**420**: 84 × 5 = 420**840**: 84 × 10 = 840**1680**: 84 × 20 = 1680

## Real-Life Examples

**Time**: 5040 seconds in 84 minutes: 84 × 60 = 5040 seconds.**Money**: $84 as 84 one-dollar bills: 84 × 1 = 84 dollars.**Measurements**: 168 inches in 14 feet: 84 × 2 = 168 inches (since 1 foot = 12 inches, 14 feet = 168 inches).

## Practical Examples of Multiples of 84

**Time Calculation**: To find how many seconds are in 84 minutes, multiply the number of minutes by 60.**84 × 60 = 5040 seconds****Budgeting**: If you have $84 bills, you have a total of 84 dollars.**84 × 1 = 84 dollars****Construction Measurement**: To convert 14 feet to inches, multiply by 12 (since 1 foot = 12 inches) and then find the multiple of 84.**14 × 12 = 168 inches****84 × 2 = 168 inches****Event Planning**: If you plan an event for 84 guests and need to allocate 2 chairs per guest, you need a total of:**84 × 2 = 168 chairs****Bulk Purchasing**: If each box contains 84 items and you buy 10 boxes, you will have:**84 × 10 = 840 items**

## Practical Applications

**Counting by Eighty-Fours**: When counting by eighty-fours (84, 168, 252, 336…), you are listing the multiples of 84.**Large Group Division**: Any large number that is a multiple of 84, such as 168 or 252, can be evenly divided by 84. For example, 168 ÷ 84 = 2, and 252 ÷ 84 = 3.

## Are multiples of 84 also multiples of 42?

Yes, multiples of 84 are also multiples of 42 because 84 is a multiple of 42.

## Is 252 a multiple of 84?

Yes, 252 is a multiple of 84 because 84 × 3 = 252.

## Can a multiple of 84 be an odd number?

No, multiples of 84 cannot be odd because 84 is an even number.

## What is the 15th multiple of 84?

The 15th multiple of 84 is 1260 (84 × 15).

## Is 1008 a multiple of 84?

Yes, 1008 is a multiple of 84 because 84 × 12 = 1008.

## How do you check if a number is a multiple of 84?

To check if a number is a multiple of 84, divide the number by 84. If the result is an integer, then it is a multiple of 84.

## What is the largest multiple of 84 under 1000?

The largest multiple of 84 under 1000 is 924 (84 × 11).

## Is 700 a multiple of 84?

No, 700 is not a multiple of 84 because 700 ÷ 84 does not result in an integer.

## What is the 20th multiple of 84?

The 20th multiple of 84 is 1680 (84 × 20).

## Are multiples of 84 divisible by 7?

Yes, multiples of 84 are divisible by 7 because 84 is a multiple of 7.

## Is 336 a multiple of 84?

Yes, 336 is a multiple of 84 because 84 × 4 = 336.