 # Factors Of 27

The factors of 27 are the numbers, which gives the number 27 when multiplied together in pair of two. Pair factors of the number 27 are the whole numbers which could be positive and negative but not a fraction or decimal number. For example, the factor of 3 is 1 & 3 and -1 & -3. When we multiply two negative factors, the resulted number is positive, such as multiplying -1 and -3, we get the number 3. Thus we can consider both positive and negative pair factors of 3. To find the factors of a number 27, we use the factorization method.

In this method, we consider 1 and 27 are the factors and continue with finding the factor pairs of 27 which results in the original number. To understand in a better way, keep reading the article and also, we will find here the prime factorisation of 27 with the help of the division method.

## Factors Of 27 in Pairs

We can find the factors in pairs of 27, by multiplying two numbers to get the original number as 27, such as:

If 1 × 27 = 27

3 × 9 = 27

Therefore, the positive pair factors of 27 are (1, 27) and (3, 9).

Now if we have to find the negative factors;

-1 × -27 = 27

-3 × -9 = 27

Therefore, the negative pair factors of 27 are (-1, -27) and (-3, -9).

### How to find the factors of 27?

Let us learn the steps to find the factors;

• First, write the number 27 in your notebook.
• Find the two numbers, which on multiplication gives 27, say 3 and 9, such as 3 × 9 = 27.
• We know 3 is a prime number which has only two factors, i.e., 1 and number itself. So, we cannot further factorize it.

3 = 1 × 3

• But 9 is not a prime number and can be further factorized.

9 = 3 × 3 × 1

• Therefore, the factorization of 27 gives us, 27 = 1 × 3 × 3 × 3.
• Write down all the unique numbers which are obtained here.
 Factors Of 27 1, 3, 9 and 27

### Prime Factorisation of 27

The number 27 is a composite number. Now let us find the prime factors of 27.

• The first step is to divide the number 27 with the smallest prime factor,i.e. 2.

27 ÷ 2 = 13.5

But, factors cannot be a fraction, therefore, 2 is not the prime factor for 27.

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

27 ÷ 3 = 9, 3 is a prime factor of 27

• Again divide 9 by 3.

9 ÷ 3 = 3

So, 3 is again a prime factor of 27.

• Again dividing 3 by 3 we get,

3 ÷ 3 = 1

• We have received 1 at the end and further, we cannot proceed with the division method. So, the prime factorisation of 27 are 3 × 3 × 3 or 33, where 3 is a prime number.