 # Factors Of 27

The factors of 27 are the numbers, which gives the number 27 when multiplied together in a 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 factors of 3 are 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 result in the original number.

## Factors Of 27 in Pairs

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

1 × 27 = 27

3 × 9 = 27

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

The negative factors are:

-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?

The steps to find the factors are:

• 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 is 3 × 3 × 3 or 33, where 3 is a prime number.