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 resulting 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 article, we will learn the factors of 27 and the pair factors and the prime factors of 27 using the prime factorization method with many solved examples.

Table of Contents:

• What are the Factors of 27?
• Pair Factors of 27
• How to Find the Factors of 27?
• Prime Factorization of 27
• Solved Examples
• FAQs

What are the Factors of 27?

The factors of 27 are the numbers that divide 27 exactly without leaving any remainder. In other words, the factors of 27 are the numbers that are multiplied in pairs resulting in the number 27. As the number 27 is a composite number, it has many factors other than one and 27. Thus, the factors of 27 are 1, 3, 7 and 27.

Pair Factors of 27

The pair factors of 27 are the numbers, which are multiplied together to get the number 27. The pair factors of 27 can be positive or negative. Thus, the positive and negative pair factors are given below:

Positive Pair Factors of 27:

Negative Pair Factors of 27:

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 that has only two factors, i.e. 1 and the number itself. So, we cannot further factorize it. (i.e.) 3 = 1 × 3

• • But 9 is not a prime number and can be further factorized. (i.e.) 9 = 3 × 3 × 1
  • Therefore, the factorization of 27 gives us, 1 × 3 × 3 × 3.
  • Write down all the unique numbers which are obtained here.

Prime Factorization 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 number, 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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Examples

Example 1:

Find the common factors of 27 and 26.

Solution:

The factors of 27 are 1, 3, 9 and 27.

The factors of 26 are 1, 2, 13 and 26.

Hence, the common factor of 27 and 26 is 1.

Example 2:

Find the common factors of 27 and 28.

Solution:

Factors of 27 = 1, 3, 9 and 27.

Factors of 28 = 1, 2, 4, 7, 14 and 28

Thus, the common factor of 27 and 28 is 1.

Example 3:

Find the common factors of 27 and 20.

Solution:

The factors of 27 are 1, 3, 9 and 27.

The factors of 20 are 1, 2, 4, 5, 10, and 20.

Hence, the common factor of 27 and 20 is 1.