 # Factors Of 84

Factors of 84 are the numbers which when multiplied in pairs gives the original number. These numbers when divides the number 84, results in quotient as a whole number. 84 is a composite number and have more than 2 factors, unlike prime numbers. Whereas multiples of 84 are the numbers, which are the extended times of 84, such as, 168, 252, 336, 420, 504, 588 and so on. This is the basic difference between factors and multiples. Now let us find out the factors in pairs along with its prime factorisation. ## Factors Of 84 In Pairs

We can find the factor pairs, by multiplying 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

Therefore, the factors pairs are (1, 84), (2, 42), (3, 28), (4, 21), (6, 14) and (7, 12). Thus, with this we can evaluate the unique factors of number 84 as given below;

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

### Prime Factorisation of 84

84 is a composite number, so let us find the prime factors present in 84.

• The first step is to divide the number 84 with the smallest prime factor,i.e. 2.

84 ÷ 2 = 42

Again, divide 42 by 2.

42 ÷ 2 = 21

Now, if we divide 21 by 2 we get a fraction number, which cannot be a factor.

• Now, proceed to the next prime numbers, i.e. 3, 5, 7 and so on.

21 ÷ 3 = 7

7 ÷ 3 = 2.33, not a factor

Move to next prime number, 5.

• Divide 7 by 5, again gives a fraction value.

7 ÷ 5 = 1.4, not a factor

Move to next prime number 7.

• Dividing 7 by 7 we get,

7 ÷ 7 = 1

• We have received 1 at the end and further, we cannot proceed with the division method. So, the prime factorisation of 84 is 2 × 2 × 3 × 7 or 22 × 3 × 7, where 2, 3 and 7 are the prime numbers.