[Maths Class Notes] on Factors of 54 Pdf for Exam

In Mathematics, factors are an algebraic expression that divides a number evenly. Dividing a number evenly means that there is no remainder after the division. 

For example, if you want to find the factors of 12, you can try to divide it by every number that is less than or equal to 12. So you can do 12÷1, 12÷2, 12÷3, etc. If any of these equations result in a number with no remainder, then that number is a factor of 12.

So in this example, the factors of 12 would be 1,2,3,4,6, and 12 because only these numbers divided 12 without any remainder.

 

Prime Factorization of 54

The factors of the number 54 are the numbers, positive or negative when two different numbers are multiplied together. Let’s consider an example for better understanding.

The factor pairs of the number 11 can be written as (1, 11) and (-1, -11). When you multiply this pair of the negative numbers, it would give you the same result as you multiply the positive numbers. Hence, you can consider both the positive as well as the negative factors of the number 11.

The factor pairs of the number 54 are whole numbers that can either be positive or negative. However, these factors cannot be a decimal numbers or an integer. For finding the different factors of a number, you can use the prime factorization method.

 

Finding the Factor Pairs of 54

 

Prime Factorization Method

The prime factorization of 54 is a method to find out the prime factors of the number 54. Firstly, consider the numbers 1 and 54 as the factors of 54 and then find out the other pairs which are the multiples of 54. This would give you the number 54 when you multiply them all. For understanding, this method in a better manner read about how you can find the factors of 54 in pairs. You can also learn below how to find the factors of the number 54 with the help of the division method.

But before we proceed, here is what you need to know about the properties of the factors.

The factors of any given number are their exact divisors. This means that the number is exactly divisible by its factors.

1. Each number has two factors, 1 and the number itself.

2. The factors are always less than or equal to the number.

3. The greatest positive factor of any positive number is that number itself.

 

Prime Factors of the Number 54 by the Division Method

Prime factorization of 54 refers to finding the prime factors of the number 54. For finding the prime factors, you need to divide the number by the least possible prime factor. The result of that number is again divided by the least possible prime factor. You need to repeat this procedure till you reach number 1.

The prime factorization of 54 results in a prime factor tree if the number 54. All the prime numbers which are used for diving in the prime factor tree are called numbers instruction a look at this illustration:

54 ÷ 2 = 27,

27 ÷ 3 = 9,

9 ÷ 3 = 3,

3 ÷ 3 = 1.

The prime numbers which you used for this division are all the prime factors of the number 54. Hence, the prime factors of 54 are:

2, 3, 3, and 3. In short, the prime factors of 54 are 2 and 3.

 

Factor Pairs of 54

The factor pairs of 54 are all the different types of combinations of two of the factors of the number 54 which you multiply and get 54 as a result.

The process for finding the factor pairs of 54 is very simple.

Firstly, you need to list down all the factors of the number 54.

Then make pairs of different combinations of these factors and it would give you the factor pairs of 54.

 

The Different Factors of 54 are:

1, 2, 3, 6, 9, 18, 27, 54.

When you make different pair combinations of these factors, it would give you the factor pairs of 54.

Take a look below at all the factor pairs of the number 54. As you notice, all these factor pairs would result in the number 54 when multiplied together.

1 x 54 = 54

2 x 27 = 54

3 x 18 = 54

6 x 9 = 54

9 x 6 = 54

18 x 3 = 54

27 x 2 = 54

54 x 1 = 54

Hence the Pair Factors of 54 are as follows:

(1,54), (2,27), (3,18), and (6,9)

 The positive pair factors of the number 54 are (1, 54), (2, 27),(3, 18), and (6, 9).

However, the number 54 also has negative factor pairs.

To find the negative pair factors of 54, proceed with the steps below:

-1 × -54 = 54

Hence, (-1, -54) is a pair factor of 54.

-2 × -27 = 54

Hence, (-2, -27) is a pair factor of 54

-3 × -18 = 54

Hence, (-3, -18) is a pair factor of 54

-6 × -9 = 54

Hence, (-6, -9) is a pair factor of 54

Therefore, the negative pair factors of the number 54 are (-1, -54), (-2, -27), (-3, -18) and

(-6, – 9).

Studying for Factors with

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