# Multiples of 84

Created by: Team Maths - Examples.com, Last Updated: May 29, 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

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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