[Maths Class Notes] on Factors of 27 Pdf for Exam

Any number or algebraic expression that can divide another number, or another algebraic expression with no remainders is called a factor, in Mathematics. This means that the division is even, since there are no remainders. 

Kinds of Factor

There are two kinds of factors:

• Prime Factor – this means that if any positive integer which is greater than 1 has only two factors, namely one and that number itself, it is called a prime factor. This means that it is not completely divisible with other numbers. For example, 2 and  are prime factors since they cannot be divided by anything other than 1, and themselves. 

• Composite Factor – this means that if any positive integer which is greater than 1 has more than two factors, it is a composite factor. Our number in question, 27, is a composite factor. 

Factors are an important concept in arithmetic. Factors of 27 are simply numbers — more than two, which upon multiplication lead to the result or product of 27. In simple terms, factors are two or more numbers which upon multiplication lead to another number.  Factors are also explored in algebra. Since algebra uses variables most of the time, the factors of an algebraic term are also in the form of variables. Factors of 27 are specifically unique in its nature. Understanding its factors through division, prime factorization is some key takeaways from this article.  

The example below can explain this further:

(x2 + 5x + 5) is an algebraic term with two factors (x+5) and (x+ 1)

Therefore, (x+5)(x+ 1) = x2 + 5x + 5

What are the Factors of 27? 

Based on what we have explained earlier, we can find the factors of 27 simply by seeing which numbers are completely divisible. Any numbers more than 1, which will yield 27 as result when multiplied together as well as leave no remainder when they are used to divide 27 will qualify as a factor. 

How can the Factors of 27 be Calculated? 

There are a number of ways to find out the factors of 27. Some of these are: 

This means we can start to divide 27 by any number greater than 1. Whichever numbers leave no remainder will automatically qualify as a factor.

For example, 

Factors of 27

In this method, we can find out the factors of 27 by listing out the factors which will yield 27 as a result when multiplied together. 

For example, if we multiply 9 and 3, we will get 27. 

• Now, we have to check whether these are prime numbers or not. 

• 3 is a prime number, so we move on to 9. 

• 9 is not a prime number, and is a product of 3 multiplied with 3. 

• Hence, we can see that 27 has four factors- 1, 3, 9 and 27 itself. 

A frequently asked question (FAQ) is whether a number can have a factor bigger than the number itself. The answer to that is no. Since factors are a multiplication of numbers that lead to another number, the factors are always smaller than the product.

A number itself is its greatest factor. The biggest factor for 27 is 27 itself. The value of the factor never exceeds the product value.

Pairs of factors is another approach of finding factors of a number. The pairs of factors for 27 can be derived from the single factors that we have found above: 1,  3, 9, and 27.

Use the approach below in order to understand the methodology behind a pair of two factors:

From the calculation above, it can be inferred that there are 2 pairs of two factors for 27. They are (1, 27) and (3, 9). You can observe that these pairs of factors have been derived originally from the factors obtained through division. Therefore, it is highly recommended that you use the division approach when attempting questions on factors.

Just as there are pairs of two factors, there are also pairs of three and more factors for a product. This approach is used to find the smallest factors of 27. Similar to pairs of two factors, we will be using the factors derived from the division method: 1,  3, 9, and 27. 

From the calculations above, we can see that there can be a pair of three factors for 27, and they are  (1, 3, 9).