Factors of 27

Factors of 27 are 1, 3, 9, and 27 itself. In mathematics, a factor is any number or algebraic expression that may divide another number or another algebraic expression with no remainders. Given that there are no remainders, this indicates that the division is even. For this let’s illustrate one example “factor of 27”, If we multiply two integers 3 and 9 together, that gives you the number 27, and Same side as we divide 27 by 9 that gives us 3.

So, In this article, we will learn about factors of 27, prime factorization, positive pairs, negative factors pairs, and other several topics.

What are the Factors of 27?

The numbers that can be multiplied together to produce 27 are the factors of 27. So, In the case of 27, the factors are 1, 3, 9, and 27. The factors of 27 are the integers that can be multiplied together to yield product 27. These numbers can divide the number 27 without leaving any remainder. In such case where 27 is perfectly divided by any integer, then both divisor and quotient are the factors of 27.

Factors of 27 Calculator

To calculate factors of 27 use the calculator below:

How to Find Factors of 27?

To find the Factors of 27 there are various methods such as Division Method or Prime Factorization method. We will discuss both of these methods in detail as follows:

Factors of 27 by Multiplication Method

Let’s obtain the factors of 27 by Multiplication Method with solved example:

• 1 × 27 = 27
• 3 × 9 = 27
• 27 × 1 = 27
• 9 × 3 = 27

Factors of 27 by Division Method

Let’s obtain the factors of 27 by Division Method with solved example:

• 27 ÷ 1 = 27
• 27 ÷ 3 = 9
• 27 ÷ 9 = 3
• 27 ÷ 27 = 1

Hence, Factors of 27 are 1, 3, 9 and 27

All Factors of 27

The entire list of 27 factors is as follows:

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

Prime Factorization of 27

Prime Factorization of a number is way of representing the number in the form of product of its prime factors. In case of 27, its prime factorization is given as

27 = 3 × 3 × 3 = 3³

The prime factorization of 27 is performed in the image attached below:

Prime Factors of 27

To get the prime factor of 27, we must divide 27 by each prime number until there is only one left. So, let’s see the prime factors of 27 in the following steps:

• Here, start with the number 27.
• Then divide 27 by the smallest prime factor, which is 3.
• After that, Divide 9 by 3 again.
• At last, Divide 3 by 3 you get 1.

So therefore the Prime factors of 27 = 3 × 3 × 3 = 3³

Learn, Prime Factorization

Factor Tree of 27

Let’s see the factor tree of 27 and how it begins.

• It starts with the number 27.
• 27 splits into 3 and 9.
• After that, 3 will remain as it is. 9 will be separated.
• At last, 9 is further split into two factors 3 and 3.

The factor tree of 27 is shown below:

Factor Pairs of 27

The original number 27 is obtained by multiplying two integers together, which is known as the factor pair of 27. Therefore, we will keep to the 27 positive and negative pair criteria for this approach.

Positive Factor Pairs of 27

Multiply the two integers in a pair to obtain the original number 27, to find the “Pair factors of Positive integers”:

• 1 × 27 = 27
• 3 × 9 = 27
• 27 × 1 = 27
• 9 × 3 = 27

The pair factors of Positive integers are (1, 27) and (3, 9).

Negative Factor Pairs of 27

Multiply the two integers in a pair to obtain the original number 27, to find the “Pair factors of negative integers”:

• -1 × -27 = 27
• -3 × -9 = 27
• -27 × -1 = 27
• -9 × -3 = 27

The pair factors of negative integers are (-1, -27) and (-3, -9).

Factors of 27 Solved Examples

Example 1: What is the sum of the factors of 27?

Solution:

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

The sum of the factors of 27 is 1 + 3 + 9 + 27 = 40.

Therefore, the sum of the factors of 27 is 40.

Example 2: If a × b = 27, find the possible values of a and b.

Solution:

Some of the possible values of a and b are:

• a = 1, b = 27; 1 × 27 = 27
• a = 3, b = 9; 3 × 9 = 27
• a = 9, b = 3; 9 × 3 = 27
• a = 27, b = 1; 27 × 1 = 27

Example 3: John spends 9 hours a day studying. How many days will he need to complete 27 hours?

Solution:

John spends 9 hours a day studying, and he wants to complete 27 hours.

So, Here we use the formula; No. of days = Total Hours/ Hours per day = 27/9 = 3 days

Therefore, John need at least 3 days to complete 27 hours.

Example 4: Express 27 as the product of its prime factors.

Solution:

27 as the product of its prime factors is expressed as 3 × 3 × 3

Factors of 27 Practice Questions

Q1: Find two numbers that multiply to give 27.

Q2: Express 27 as the product of its prime factors.

Q3: Determine if 5 is a factor of 27.

Q4: List the positive factor pairs of 27.

Factors of 27 Frequently Asked Questions

What are the Factors of 27?

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

What are the Prime Factors of 27?

The prime factorization of 27 can be expressed as 3 × 3 × 3. Hence its prime factor is 3.

^{Is 5 a factor of 27?}

No, 5 is not a factor of 27.

What are the Positive Factor Pairs of 27?

The positive factor pairs of 27 are (1, 27) and (3, 9).

Is 2 a Factor of 27?

No, 2 is not a factor of 27.

What are the Common Factors of 27 and 36?

The common factors of 27 and 36 are 1, 3, and 9.