# Factors of 84 in pair

Factors of 84 in pair are (1, 84) , (2, 42) , (3, 28) , (4, 21) , (6, 14) and (7, 12)

#### How to find factors of a number in pair

 1.   Steps to find factors of 84 in pair 2.   What is factors of a number in pair? 3.   What are Factors? 4.   Frequently Asked Questions 5.   Examples of factors in pair

### Example: Find factors of 84 in pair

Factor Pair Pair Factorization
1 and 84 1 x 84 = 84
2 and 42 2 x 42 = 84
3 and 28 3 x 28 = 84
4 and 21 4 x 21 = 84
6 and 14 6 x 14 = 84
7 and 12 7 x 12 = 84

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 84. They are called negative pair factors.

Hence, the negative pairs of 84 would be ( -1 , -84 ) .

#### What does factor pairs of a number mean?

Factor pairs are those factors in pair that can give original number when multiplied. Every natural number is a product of atleast one factor pair. Eg- Factors of 84 are 1 , 2 , 3 , 4 , 6 , 7 , 12 , 14 , 21 , 28 , 42 , 84. So, factors of 84 in pair are (1,84), (2,42), (3,28), (4,21), (6,14), (7,12).

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of Factors

• Each number is a factor of itself. Eg. 84 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 84.
• Every number is a factor of zero (0), since 84 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 are exact divisors of 84.
• Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. Each factor divides 84 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 are all less than or equal to 84.

#### Steps to find Factors of 84

• Step 1. Find all the numbers that would divide 84 without leaving any remainder. Starting with the number 1 upto 42 (half of 84). The number 1 and the number itself are always factors of the given number.
84 ÷ 1 : Remainder = 0
84 ÷ 2 : Remainder = 0
84 ÷ 3 : Remainder = 0
84 ÷ 4 : Remainder = 0
84 ÷ 6 : Remainder = 0
84 ÷ 7 : Remainder = 0
84 ÷ 12 : Remainder = 0
84 ÷ 14 : Remainder = 0
84 ÷ 21 : Remainder = 0
84 ÷ 28 : Remainder = 0
84 ÷ 42 : Remainder = 0
84 ÷ 84 : Remainder = 0

Hence, Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84

• Is 84 a composite number?

Yes 84 is a composite number.

• Is 84 a prime number?

No 84 is not a prime number.

• What is the mean of factors of 84?

Factors of 84 are 1 , 2 , 3 , 4 , 6 , 7 , 12 , 14 , 21 , 28 , 42 , 84. therefore mean of factors of 84 is (1 + 2 + 3 + 4 + 6 + 7 + 12 + 14 + 21 + 28 + 42 + 84) / 12 = 18.67.

• What do you mean by proper divisors?

A number x is said to be the proper divisor of y if it divides y completely, given that x is smaller than y.

• What do you mean by improper divisors?

An improper divisor of a number is the number itself apart from this any divisor of a given number is a proper divisor.

#### Examples of Factors

Rustom has been assigned the following tasks by the teacher:
- Finding out all positive factors of 84.
- Writing all prime factors of 84.
- Writing all the possible factors of 84 in pair.
Help him in writing all these.

Positive factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
Prime factors of 84 are 2, 2, 3, 7.
Factors of 84 in pair are (1,84), (2,42), (3,28), (4,21), (6,14), (7,12).

What are the pair factors of 84?

Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. Hence, the factors of 84 in pair are (1,84), (2,42), (3,28), (4,21), (6,14), (7,12).

Can you help Sammy list the factors of 84 and also find the factor pairs?

Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
Factors of 84 in pair are (1,84), (2,42), (3,28), (4,21), (6,14), (7,12).

The area of a rectangle is 84 square meters. List all the possible combinations possible for length and breadth in which a designer can design out all the combinations.

For the possible combinations possible for length and breadth in which a designer can design out all the rectangles can be calculated by calculating the factors of 84 in pair. So, the possible combinations (1,84), (2,42), (3,28), (4,21), (6,14), (7,12).

Help Diji in finding factors of 84 by Prime Factorization method and then sorting factors of 84 in pairs.

Prime factorization of 84 is 2 x 2 x 3 x 7. Factors of 84 in pair can be written as (1,84), (2,42), (3,28), (4,21), (6,14), (7,12).

Write the smallest prime factor of 84.

Smallest prime factor of 84 is 2.

Write the largest prime factor of 84.

Largest prime factor of 84 is 7.

Diji wants to write all the negative factors of 84. Can you help Diji in doing the same?

Negative factors of 84 are -1, -2, -3, -4, -6, -7, -12, -14, -21, -28, -42, -84.