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.

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