January 6th, 2022 | Updated on August 5th, 2022
Here is a compilation of all the details you could need on prime factors of 120. We’ll highlight the definition of the Prime Factors of 120, demonstrate how to identify the Prime Factors of 120 through the creation of a Prime Factor Tree of 120.
We’ll also determine how many Prime Factors in 120 exist and reveal some other facts about this topic such as definition and the technique of finding it.
What Exactly Is Prime Factorization?
A prime factorization is an approach to finding all the factors that make up numbers so that the initial number is equally divided through these elements.
As we all know, the composite number is composed of at least two factors, so this method can only be used for composite numbers, not for prime numbers.
For instance, the prime factors of 126 would be 2,3 and 7 because 2 x 3 x 3 7 = 126. 2, 3, 7 are prime numbers.
Anther example, prime factorization of
- 12 is 2 times 2 and 3 = 22 3
- 18 is 2 3 3 = 2 32
- The 24th digit is 2x 2x 3 = 23 x 3.
- 20 is 2 times 2×5 = 22 5
When multiplied with any natural number and entire numbers (but not zero), the prime numbers create composite numbers. This is a prime factorization applied to the composite numbers to factorize them and then find their prime factorization.
This technique can also be used when trying to find the HCF (Highest Common Factor) and the LCM (Least Common Multiple) for any number set.
If two numbers are presented, the number with the highest common factor will be considered the biggest factor in both numbers. The most common multiple is the least common multiple of both numbers.
Prime Factors Of The 120 Definition
It is essential to note that prime numbers comprise all integers positive that can be divided by 1 and by themselves. The Prime Factors are just prime numbers that, when you multiply, become equal to 120. This was the perfect definition of the Prime Factorization of 120.
How Do You Find The Prime Factors Of 120?
The method of determining prime factors of 120 is known as Prim factorization 120. To find the Prime Factors for 120, you will divide 120 by the smallest number of prime numbers that you can find. Then, you subtract the result and divide that number by the number that is the smallest.
Repeat the process until you have 1.
The Prime Factorization process produces what we refer to as”the Prime Factor Tree of 120.
All prime numbers utilized to divide within the tree of Prime Factors are Prime Factors. Here’s the math used to illustrate:
120 / 2 = 60
60 x 2 = 30
30 / 2 = 15
15/3 = 5
5 + 5 = 10
Also, all the prime numbers you divided over are prime factors of 120. Therefore the Prime Factors of 120 are:
2, 2, 2, 3, 5.
How Many Prime Factors Of 120?
If we look at the number of prime numbers above, we discover that 120 is the sum of five prime factors.
Prime Factors: Product Of 120
These Prime Factors are exclusive to 120. When you multiply all of the Prime Factors in 120, it will give you 120. This is referred to as the product of prime factors of 120. Here is the product of Prime Factors of 120:
2 x 2 x 2 x 3 5 = 120
Techniques For Finding Prime Factorization
There are many ways to determine the prime factorization of numbers. The most popular methods used to determine the prime factorization are listed below:
- Prime factorization with factor tree method
- Method of Division of Prime Factorization
Prime Factorization Using Factor Tree Method
When using the factor tree method, the factors of a particular number are determined, and then the numbers are factored until we get to what is known as prime numbers. To assess whether a prime factorization is possible for a particular number using the method of factor trees, take the steps below:
- Step 1: Take that number in terms of the tree’s root, which lies at the highest point of the tree.
- Step 2: Note down the pair of factors as branches of the tree.
- Step 3: Calculate the factors in the composite that you discovered in step 2 and note down the two factors that will form the following branches of the tree.
- Step 4: Continue step 3 until we reach the primary elements of all those composite elements.
Method Of Division For Prime Factorization
The division method can be used to identify the primary factors in a number by dividing them with a prime number. Follow the steps listed below to identify those prime elements of a particular number through the method of division.
- Step 1: Divide the number by the number with the lowest prime value, such that the prime number with the lowest number will divide the number in entirety.
- Step 2: Once again, divide the quotient from Step 1 with the smallest number in prime numbers.
- Step 3: Keep repeating step 2 until you get quotient 1.
- Step 4: Thus, add all principal factors, which are divisors of division.
Another Easy Example Of Factorization
Question:
Emily must demonstrate that the prime factorization for 40 will stay the same. She is confused; please help her prove it.
Solution:
Emily uses the division method and the factor tree method to show that the prime factorization of 40 will remain the same. Jane is aware that 40 could be factored in 5 and 8.
The number 8 is a composite number that can be further broken down as the product of 4 and 2. 5. A 5th number is already a prime number. So, she will explain how to use the divide method and the factor tree method in this method:
This means that notwithstanding the method used for factorization, the prime factorization is the same. The prime factorization of an individual number is different.
Conclusion
Understanding prime factorizations shouldn’t be an easy task. It’s all about knowing how this technique operates.
Once you’ve grasped the method, it shouldn’t be difficult for you to perform factorizations with even large numbers.
Make sure you are prepared for factorizations since they are always part of the examinations (in your syllabus). It’s an ideal opportunity to score points!
