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

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.