Multiples of 84

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Created by: Team Maths - Examples.com, Last Updated: August 22, 2024

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:

NumberReasonRemainder
8484 × 1, which equals 84, making it a multiple of 840
16884 × 2, which equals 168, making it a multiple of 840
25284 × 3, which equals 252, making it a multiple of 840
33684 × 4, which equals 336, making it a multiple of 840
132132 ÷ 84 is not an integer, thus 132 is not a multiple of 8448

List of First 100 Multiples of 84 with Remainders

NumberReasonRemainder
8484 × 1, which equals 840
16884 × 2, which equals 1680
25284 × 3, which equals 2520
33684 × 4, which equals 3360
42084 × 5, which equals 4200
50484 × 6, which equals 5040
58884 × 7, which equals 5880
67284 × 8, which equals 6720
75684 × 9, which equals 7560
84084 × 10, which equals 8400
92484 × 11, which equals 9240
100884 × 12, which equals 10080
109284 × 13, which equals 10920
117684 × 14, which equals 11760
126084 × 15, which equals 12600
134484 × 16, which equals 13440
142884 × 17, which equals 14280
151284 × 18, which equals 15120
159684 × 19, which equals 15960
168084 × 20, which equals 16800
176484 × 21, which equals 17640
184884 × 22, which equals 18480
193284 × 23, which equals 19320
201684 × 24, which equals 20160
210084 × 25, which equals 21000
218484 × 26, which equals 21840
226884 × 27, which equals 22680
235284 × 28, which equals 23520
243684 × 29, which equals 24360
252084 × 30, which equals 25200
260484 × 31, which equals 26040
268884 × 32, which equals 26880
277284 × 33, which equals 27720
285684 × 34, which equals 28560
294084 × 35, which equals 29400
302484 × 36, which equals 30240
310884 × 37, which equals 31080
319284 × 38, which equals 31920
327684 × 39, which equals 32760
336084 × 40, which equals 33600
344484 × 41, which equals 34440
352884 × 42, which equals 35280
361284 × 43, which equals 36120
369684 × 44, which equals 36960
378084 × 45, which equals 37800
386484 × 46, which equals 38640
394884 × 47, which equals 39480
403284 × 48, which equals 40320
411684 × 49, which equals 41160
420084 × 50, which equals 42000
428484 × 51, which equals 42840
436884 × 52, which equals 43680
445284 × 53, which equals 44520
453684 × 54, which equals 45360
462084 × 55, which equals 46200
470484 × 56, which equals 47040
478884 × 57, which equals 47880
487284 × 58, which equals 48720
495684 × 59, which equals 49560
504084 × 60, which equals 50400
512484 × 61, which equals 51240
520884 × 62, which equals 52080
529284 × 63, which equals 52920
537684 × 64, which equals 53760
546084 × 65, which equals 54600
554484 × 66, which equals 55440
562884 × 67, which equals 56280
571284 × 68, which equals 57120
579684 × 69, which equals 57960
588084 × 70, which equals 58800
596484 × 71, which equals 59640
604884 × 72, which equals 60480
613284 × 73, which equals 61320
621684 × 74, which equals 62160
630084 × 75, which equals 63000
638484 × 76, which equals 63840
646884 × 77, which equals 64680
655284 × 78, which equals 65520
663684 × 79, which equals 66360
672084 × 80, which equals 67200
680484 × 81, which equals 68040
688884 × 82, which equals 68880
697284 × 83, which equals 69720
705684 × 84, which equals 70560
714084 × 85, which equals 71400
722484 × 86, which equals 72240
730884 × 87, which equals 73080
739284 × 88, which equals 73920
747684 × 89, which equals 74760
756084 × 90, which equals 75600
764484 × 91, which equals 76440
772884 × 92, which equals 77280
781284 × 93, which equals 78120
789684 × 94, which equals 78960
798084 × 95, which equals 79800
806484 × 96, which equals 80640
814884 × 97, which equals 81480
823284 × 98, which equals 82320
831684 × 99, which equals 83160
840084 × 100, which equals 84000

Read More About Multiples of 84

Table 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

  1. Time Calculation: To find how many seconds are in 84 minutes, multiply the number of minutes by 60.
    84 × 60 = 5040 seconds
  2. Budgeting: If you have $84 bills, you have a total of 84 dollars.
    84 × 1 = 84 dollars
  3. 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
  4. 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
  5. Bulk Purchasing: If each box contains 84 items and you buy 10 boxes, you will have:
    84 × 10 = 840 items

Practical Applications

  1. Counting by Eighty-Fours: When counting by eighty-fours (84, 168, 252, 336…), you are listing the multiples of 84.
  2. 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.

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