What are the Factors?
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.
Each number has two factors, 1 and the number itself.
The factors are always less than or equal to the number.
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 Vedantu
You can study Factors by using the numerous resources available on Vedantu. On this particular page, you will find a detailed set of instructions on how to find the factors and factor pairs for the number 54. You can find more resources like this on the Vedantu website or app. Just use the navigation menu or search bar to find the materials you need. Most of it should be under the tab Study Materials in the navigation menu.
If you're looking for 1 on 1 instruction, you can even book a class where you will get expert instructions and lessons in Maths. This will help you learn faster and you will be able to benefit from Vedantu's expert-quality guidance.
For more information about Factors, click here.
FAQs on Factors of 54
1. How can you Calculate the Factors of 54?
You can easily calculate the factors of the number 54 by following these steps:
The first step is to note down the number 54.
Then, follow the prime division method by dividing the number 54 with the lowest possible prime number. The first two numbers when multiplied would give you the number 54 as a result.
Take the numbers 2 and 27. When you multiply together, it would give you the number 54.
The number 2 cannot be factorized further, so you can leave it as it is. However, the number 27 is composite and has factors.
2 x 1 = 2
Continue factorizing 27 further with the least prime number.
Factorizing 27 would give you
27: 3 x 3 x 3 x 1
When you multiply all these factors together it would result in the number 54.
Hence you can write the factorization of 54 in the following manner:
54 = 2 x 3 x 3 x 3 x 1.
2. How should you study for Factors of 54?
To study for Factors of 54, you can refer to the information given on this page. Above, you will find a simple explanation of what factors are, how to calculate the factors of 54 through different methods, and what the factors of 54 are. You can also look through the Vedantu website for more resources to study for Maths and factors in particular. For example, if you want a detailed set of instructions and information about factors in Maths, particularly prime factors, you can click here.
3. Where to find more resources to study Factors?
To find more resources to study Factors, look no further! Vedantu has a wide range of resources available for free for all students. All you need to do is browse through the website to find them. You can use the navigation bar at the top of the page (or on the side if you're on your phone) and use the drop-down menus to find the resources you want. Alternatively, you could also use the search bar to find specific chapters or documents.
4. Are the resources on Factors on Vedantu available for free?
Yes, the resources on Factors are freely available on Vedantu! However, before you can download any materials from the website or app, you will need to sign in to your account first. If you don't have a Vedantu account, you can create one for free. Just use your email ID or phone number to sign up and follow the instructions.
If you need more instructions on how to find the factors of a number, you can click here for a detailed set of instructions.
5. What are the methods used to find factors of a number?
There are two easy ways to find the factors of a number. The first is through Division while the second is through Multiplication.
To find the factors of a number by Division, here are the steps to follow:
Keep in mind all numbers are less than or equal to the number for which you need to find the factors. For example, if the number is 6, consider all the numbers 1,2,3,4,5, and 6.
Divide the number by each number considered. For example 6÷1, 6÷2, etc.
Observe whether anything is remaining after the division. For example, 6÷3 leaves no remaining number that can't be further divided by 3. So the remainder, in that case, is 0. However, 6÷4 leaves a remainder of 2.
Keep in mind that the numbers used in this method are only whole numbers, so no decimal numbers are allowed.
If the number can be divided with no remainder, then the dividing number is one of its factors. Using the above example, 3 is one of the factors of 6 but 4 is not.
To find the factors of a number using the multiplication:
Keep in mind the number for which you need to find the factors. For this example let's take 15.
Now try to form multiplication equations that would result in the number 15. For example 1 x
× 15 = 15, 3 × 5 = 15, etc.
If you can multiply a number in such a way that it equals 15 without any remainder, then that is one of the factors of 15.
Again, keep in mind that this method only involves whole numbers