Which number is a factor of 84?

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

Step-by-step explanation:

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 factor 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 the prime factors of 84 can be found using the below steps.

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.

Dividing 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 for the division. So, the prime factorization of 84 is 2 × 2 × 3 × 7 or 22 × 3 × 7, where 2, 3 and 7 are the prime numbers.

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