Factors of 84 | with Easy division and prime factorization

Factors Of 84

The factors of 84 are the numbers that evenly divide the original number.

As an example, 2 is the factor of 84, since 84 divided by 2 equals 42. Pair factors are numbers that, when multiplied together, give the original number. As an example, 2 and 42 are pair factors.

 Let’s learn how to find the factors and pair factors along with prime factors. I hope you will learn perfectly.

What are the Factors of -84?

When we multiply two numbers, and we get -84 as a product, those numbers are the factors of -84. 

Here is the explanation:

-1 × 84 = -84

1 × -84 = -84

-2 × 42 = -84

2 × -42 = -84

-3 × 28 = -84

 3 × 28 = -84

-4 × 21 = -84

4 × -21 = -84

-6 × 14 = -84

6 × -14 = -84

-7 × 12 = -84

7 × -12 = -84

We can get -84 by having (-1, 84), (-2, 42), (-3, 28), (-4, 21), (-6, 14), and (-7, 12) as a pair of factors. Similarly, we can also get -84 by having (1, -84), (2, -42), (3, -28), (4, -21), (6, -14), and (7, -12) as a pair of factors.

Pair Factors of 84

In order to find the factor pairs, multiply two numbers in a pair to get the original number as 84, such as:

1 × 84 = 84

2 × 42 = 84

3 × 28 = 84

4 × 21 = 84

6 × 14 = 84

7 × 12 = 84

Thus, the factor pairs are (1, 84), (2, 42), (3, 28), (4, 21), (6, 14), and (7, 12). So, we can evaluate the unique factors of number 84 as follows:

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

As a pair factor of 84, we can also write a negative number since after multiplying two negative factors, we will get a positive number.

(-1) × (-84) = 84

(-2) × (-42) = 84

(-3) × (-28) = 84

(-4) × (-21) = 84

(-6) × (-14) = 84

(-7) × (-12) = 84

As a result, the negative pair factors are (-1, -84), (-2, -42), (-3, -28), (-4, -21), (-6, -14), and (-7, -12).

How to Calculate the Factors of 84?

To find the factors, we need to divide the original number by all the natural numbers until we get a quotient equal to 1.

84 ÷ 1 = 84

84 ÷ 2 = 42

84 ÷ 3 = 28

84 ÷ 4 = 21

84 ÷ 6 = 14

84 ÷ 7 = 12

84 ÷ 12 = 7

84 ÷ 14 = 6

84 ÷ 21 = 4

84 ÷ 28 = 3

84 ÷ 42 = 2

84 ÷ 84 = 1

Thus, the required factors are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84.

Prime Factorization of 84

Since 84 is a composite number, we can find its prime factors using the steps below.

• To begin, divide 84 with the smallest prime factor, i.e., 2.

84 ÷ 2 = 42

          Divide 42 by 2 once more.

42 ÷ 2 = 21

         We get a fraction if we divide 21 by 2, so it cannot be a factor.

• Next, we will look at prime numbers 3, 5, 7, and so on.

21 ÷ 3 = 7

7 ÷ 3 = 2.33, not a factor.

          Move to the next prime number, 5.

Again, dividing 7 by 5 gives a fraction value.

7 ÷ 5 = 1.4, not a factor.

         We move on to prime number 7.

• When we divide 7 by 7, we get:

7 ÷ 7 = 1

• As a result, we are unable to proceed with the division. So, 84 is a prime factorization of 2 × 2 × 3 × 7 or 22 × 3 × 7, where 2, 3, and 7 are prime numbers.

Solved Examples

Q.1: If Ali has 84 candies and has to distribute those to 7 members of the house, including her, how many candies each member gets?

Solution:

 Number of candies, Ali has = 84 

Members in the house including Ali = 7

Therefore, each member will get = 84/7 = 12candies.

Q.2: What are the factors of 84 and 92?

Answer: 

Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.

Factors of 92 = 1, 2, 4, 23, 46, and 92.

The common factors of 84 and 92 are 1,2, and 4.

Example:

Calculate the common factors of 84 and 24.

Solution:

Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.

Find the prime factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24.

As 71 is a prime number, the common factor of 84 and 24 is 1, 2, 3, 4, 6, and 12.

Example:

Calculate the common factor of 52 and 35.

Solution:

Factors of 52 = 1, 2, 4, 13, 26, and 52.

All Factors 35 = 1, 7, 5, and 35.

As a result, 70 and 35 have 1, and 7 common factors.

FAQs