Factors Of 27 | Easy Factors Pairs and Prime Factors

Factors Of 27

Factors of 27 are the numbers, which, when multiplied together in pairs of two, give the number 27. A pair factor is a whole number that can be positive or negative, but not a fraction or decimal.

 Among the factors of 3 are 1 & 3 and -1 & 3. Multiplying two negative factors yields a positive number, such as multiplying -1 and -3, and we get 3. Consequently, we can consider both positive and negative pair factors of 3. 

You use the factorization method to find the factors of 27. Using the prime factorization method with many solved examples, we will learn the factor of 27.

What are the Factors of 27?

Numbers that divide 27 exactly without leaving any remainder are called factors of 27. More specifically, the 27 factors are the pairs of numbers multiplied together to produce 27. Due to its composite nature, 27 has many factors besides one and 27. The factors of 27 are 1, 3, 7, and 27.

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

Prime Factorization of 27: 3×3×3 or 3³.

What are the Factors Of -27?

Factors of -27: -1, -3, -9, and -27.

We can get -27 by having (-1, 27), and (-3, 9) as a pair of factors. Similarly, we can also get -27 by having (1, -27) and (3, -9) as a pair of factors.

Pair Factors of 27

To get the number 27, the pair factors are multiplied together. You can combine both positives and negatives to form 27. As such, here are the factors of the positive and negative pairs:

Positive Pair Factors of 27:

Negative Pair Factors of 27:

How to Find the Factors of 27?

Finding the factors involves the following steps:

• Start by writing the number 27 in your notebook.
• Find two numbers that, when multiplied together, give 27, such as 3 and 9, such as 3  ×  9.
• As far as we know, 3 has only two factors – 1 and the number itself. Thus, it cannot be factored any further. 

So 3 = 1 × 3

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

  9 = 3 × 3 × 1

• As a result of factoring 27, we get 1 × 3 × 3 × 3.

Prime Factorization of 27

In mathematics, 27 is a composite number. Here you can find prime factors of 27.

• In the first step, divide 27 by the smallest prime number, i.e., 2.

27 ÷ 2 = 13.5

However, factors cannot be fractions, so 2 cannot be the prime factor for 27.

• Continue with prime numbers 3, 5, 7, and so on.

27 ÷ 3 = 9,   3 is a prime factor of 27

• Divide 9 by 3 once more.

9 ÷ 3 = 3

Thus, 3 is again a prime factor of 27.

• Divide 3 by 3 again, and you get:

3 ÷ 3 = 1

Since we received 1 at the end, we cannot continue with the division method. As a result, the prime factorization of 27 is 3 × 3 × 3 or 3³, in which 3 is a prime number.

Examples

Example 1:

What is the common factor between 27 and 26?

Solution:

27 has factors 1, 3, 9, and 27.

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

As a result, 27 and 26 have the same common factor of 1.

Example 2:

Identify the common factor of 27 and 24.

Solution:

There are three factors of 27: 1, 3, and 9.

1, 2, 3, 4, 6, 8, 12, and 24 are the factors of 24.

Therefore, the common factor between 27 and 24 are 1, and 3.

Example 3:

Calculate the common factors of 27 and 75.

Solution:

There are three factors in 27: 1, 3, and 27.

Factors of 75 are 1, 3, 5, 15, 25, and 75..

Therefore, 27 and 75 have common factors of 1 and 3.

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