In arithmetic, determining an HCF/LCM for two figures used frequently in the study of fractions, percentages, and other ratios required being aware of using factorisation of the number. Therefore, factoring numbers could be extremely helpful in solving a variety of issues.
Like algebra, factoring can be an extremely effective tool that is employed at all levels. It is a method that can be used to solve quadratic equations as well as reduce complex expressions. It can also be helpful for graphing functions.
Get thorough insight into the Factors of 72.
Page Contents
What Are Factor Pairs?
A factor pair could be described as a mixture of two elements multiplied to make 72. In mathematical terms, 72 is the product, and the two numbers that can be added together to make it are called the factors.
To determine the factors of 72, we have to find all the factors in 72. The complete list of factors that make 72 is 36, 24, 18, 12, 9, 8, 6, 4, 3, 2, and1. Once you have a list comprising the factors, you can make a list of all the factor pairs.
Factors of 72 Definition
When we speak of factor 72 in the context of factors, we refer to all the negative and positive factors of 72 (whole numbers), which can be equally broken down into 72. If you split 72 by one factor, the result is another factor of 72.
Let’s examine how to identify all the elements of 72 and then list them all out.
What are the Factors of 72
- Because 72 is a composite number, it contains greater than two elements.
- The factors of 72 represent numbers that divide 72 and do not leave any remainder.
- 72 has 12 components comprising 72, 36, 18, 12, 9, 8, 6, 4, 3, and 1.
- Division can be used to determine if 24, 18 and 4 are all factors of 72. Since they do not leave any remainder and leave no remainder, they are the 72 factors!
Factor Pairs of 72
Factor pairs are a mixture of two variables that can be multiplied to make 72. To get 72 factors, everyone the possible factors are given below:
- 1 x 72
- 2 x 36
- 3 x 24
- 4 x 18
- 6 x 12
- 8 x 9
Factors of 72 in Pairs
- The pair factors of 72 are all numbers multiplied to create an original figure, i.e. “72.
- Pair factors can be positive/negative, but they are not an integer or fractional numbers.
- There are 12 pairs of factor combinations of 72.
Note in the negative factor pairs that since we are multiplying a plus with a minus. The outcome is positive.
There you go—a complete guide to the variables of 72. Now you should have the expertise and knowledge to calculate your factors and factors for whatever number you’d like.
You are welcome to use the calculator to test another number. If you’re feeling creative, get an eraser and paper and attempt it with your hands. Be sure to select tiny numbers!
Important Notes
It is only complete numbers as well as integers that can be converted into factors.
- Each factor in a given number is either less or equal to that number.
- The only two numbers can contain at least two variables.
- Several elements in an unspecified number are not finite. 72 contains 12 factors.
Tips and Tricks
- 72 = 2 x 2 x 2 x 3 x 3 = 2(3)x3(2).
- Add one to both exponents individually, and multiply the sums. (3 +1) x (2 +1) = 4 x 3 = 12. This is the total number of factors that make up 72.
- Utilising prime factorisation, you can obtain all the primary factors for 72 and then multiply the prime factors in any way to obtain all 12 factors as 72, 36, 24, 18, 12, 9, 8, 6, 4, 3, 2, and 1.
Factors of 72 by Prime Factorization
Prime factorisation is the term used to describe an aggregate number as the sum of its prime elements.
- 1st step: The beginning step is to split 72 by the prime factor that is the least such as 2.
- 72 / 2 = 36
- 2nd Step: Divide another time by 2.
- 36 / 2 = 18
- 3rd Step: Divide the 18th time by 2.
- 18 / 2 = 9
- 4th Step: 9 / 2 = 4.5. When we multiply 9 times 2, we’ll get an integer fraction. A factor can’t be a fraction or a decimal number. Then, move on to your next factor of prime importance, for example, 3.
- That is 9 / 3 = 3
- 5th Step: Similarly, 3 / 3 = 1
- 6th step: We are unable to proceed since we have gotten 1 as a percentage.
- 7th Step: The primary factors 72 refer to as 2x2x3x3=
- 2(3)x3(2)+2(3)x3(2), in which 2 and 3 represent prime numbers.
It is also possible to find the prime factors by using the method of a factor tree. The top and bottom of a factor tree represent all principal factors of the original number.
There are multiple ways of creating the factor tree. Here are some additional factor trees that have the same 72
- These prime elements are enclosed in the tree of factors.
- Thus, the principal elements of 72 are described as 72 =2 x 2 x 2 x 3 x 3.
- Once we’ve done an initial factorisation, 72. We can now multiply them to get all of the additional composite variables.
Conclusion
While expanding is a common practice, factoring can be a challenge. The learner requires deep practice to master the various forms of factorisation that can arise and understand the techniques to use and the proficiency to apply these methods.
On some occasions, you may not get any common factor of each term in a given expression. However, it may be helpful to factor in pairs. So, that’s all under factorisation of 72 for today!