Factors of 84—with Easy division and prime factorization

ECTI Pakistan - Factors of 84

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. 

ECTI Pakistan - Factors of 84

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:

ECTI Pakistan - Factors of 84 in pairs

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.

ECTI Pakistan - Factors of 84 by prime factorization
  • 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 114?

Answer: 

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

Factors of 114 = 1, 2, 3, 6, 19, 38, 57, 114.

The common factors of 84 and 114 are 1,2,3, and 6.

Link Related Factors
Factors of 30 = 1,2,3,5,6,10,15 and 30.24 all factors = 1, 2, 3, 4, 6, 8, 12 and 24.92 all factors = 1, 2, 4, 23, 46, and 92.
Factors of 36 = 1,2,3,4,6,9,12,18, and 36.Factors of 38= 1, 2, 19, 38.Factors of 42 = 1, 2, 3, 6, 7, 14, 21, and 42.
Factors of 45 = 1, 3, 5, 9, 15, and 45.Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.All Factors 35 = 1, 7, 5, and 35.
Factors of 50 = 1, 2, 5, 10, 25, 50.Factors of 54 = 1, 2, 3, 6, 9, 18, 27 and 54.Factors of 56 = 1, 2, 4, 7, 8, 14, 28 and 56.

FAQs

What are the factors of 84?

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

Factors and Multiples of 84 are the same. True or False?

False. The factors and multiples of 84 are not the same.

What are the multiples of 84 in Maths?

The multiples of 84 = 84 168 252 336 420 504 588 672 756 and 840.

What are the common factors of 98 and 84?

Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
Factors of 98 = 1, 2, 7, 14, 49, 98.
The common factors of 98 and 84 are 1, 2, 7, and 14.

What is the greatest prime factor of 84?

84 has a prime factorization of 2 × 2 × 3 × 7. Thus, the largest prime factor is 7.