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Factors of 60

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Last updated date: 22nd May 2024
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Introduction

The factors are the set of numbers that produce the original number when multiplied together. To understand the factors better, it is necessary to understand the concept of prime numbers thoroughly. A prime number is a number that is only divisible by 1 and itself. For example, the numbers 2, 3, 5, and 7 are prime numbers because they are only divisible by themselves and the number 1. Therefore, Prime numbers are not the same as even numbers. A prime factorisation breaks up a number into a product of prime numbers. 


What are The Factors of 60?

Factors of 60, in mathematics, denote a combination of numbers or algebraic expressions, which when multiplied together, produces the number in the discussion.  In other words, the number divides 60 evenly without having any remainder. The number 60 is a composite number that has many divisors other than 1 and itself. It is also a positive integer that is obtained by multiplication of two smaller positive integers. Let us look into factors of 60 using the example mentioned below in the box. 


Solved example: 60 /12 = 5, and there is no remainder left. So, we can say that 12 and 5 are the factors of 60. 


Explanation Using Example Cited Above 

In the given example, we can further simplify and split the number 12 into its factors, which are 3, 2, and 2. It implies that when we multiply 3, 2, 2, and 5, we can still achieve the result 60. Thus, the factors of 60 are 5, 3, 2, and 2. Besides, 5 x 3 =15, which is also a factor of 60. So, is 4 a factor of 60? The answer is yes, because 2 x 2 = 4. Similarly, there are many other factors of 60. 


We can also derive the prime factors of 60 as it is a composite number. Apart from the number 60, there are several other numbers, such as 12, 24, 18, 48, etc., which are composite numbers and have more than 2 factors. The multiples of 60 represent the extended form of 60, such as 60, 120, 180, 240, 300, 360, 420, 480, 540, and more. 


What are the Factors of 60 in Pairs?

We can easily find the factors of a number through a simple multiplication method. So, if you are thinking about what are the factors of 60, the answer is quite straightforward.  It basically encompasses the multiplication of a pair of a number to get the end result, suppose 60. These pairs of numbers are regarded as factors. In this article, we will be actually finding what are the factors of 60 in pairs. 


How to Calculate the Factors Pairs of 60?

If you want to find out what are the factors of 60, then you have to proceed with the multiplication of two numbers in a combination that generates the result as 60. Let’s start the calculation to find out what are the pairs of 60:


Factors Pairs of 60

1 × 60 = 60

2 × 30 = 60

3 × 20 = 60

4 × 15 = 60

5 × 12 = 60

6 × 10 = 60


Hence, the factors of 60 in pairs are (1, 60), (2, 30), (3, 20), (4, 20), (5, 12), and (6, 10).


Concept of Prime Factors

The factors are the set of numbers that, when multiplied together, produce the original number. 


Now, if you want to factorize a number, you have to break it down into smaller parts. To get the prime factorization of a number, you have to break it into the prime numbers. A number which has only two factors, 1 and itself, and is only divisible by these two is called a prime number.


Prime Factors of 60

The number 60 falls into the category of a composite number. Let’s find the prime factors of 60 through calculation. To obtain the prime factors of 60, the first step involves dividing 60 by the smallest prime factor.


60 ÷ 2 = 30


Now we have to find out whether 30 can be further divided by 2 or not.


30 ÷ 2 = 15


15 ÷ 2 = 7.5


However, fractions cannot be regarded as factors. So, we need to move to the next prime number, which is 3. 


After dividing 15 by 3, we get


15 / 3 = 5


Again, dividing 5 by 3, we will get a fraction. Now, the next prime number, 5, has to be taken into consideration. 


5 / 5 = 1


As we have received 1 at the end, we cannot go ahead with the division method, because the multiple of 1 is 1. So, the prime factor of 60 is 2 x 2 x 3 x 5, which can be also written as 22 × 3 × 5. 


What is a Factor Tree of 60? 

The composite numbers can be broken into a structure of prime numbers. For the number 60, the prime factors will constitute the factor tree of 60. 


Fun Facts About Factorization:

  • Factors are integers or whole numbers, but they cannot be decimals or fractions.

  • All even numbers will have a factor as number 2.

  • All numbers greater than 0 and finishing with a 0 will have factors like 2, 5, and 10.

  • Many algebraic expressions are often simplified or solved by factoring.

  • If you want to factorize a number, you have to break it into smaller parts. For example, to get a number’s prime factorisation, you have to break it into prime numbers. A number with only two factors, 1 and itself, and only divisible by these two is called a prime number. 

  • Factors of 60 in mathematics denote a combination of numbers or algebraic expressions that produce the number in the discussion when multiplied together. 

  • Factors of 60 are the pair of numbers that give the original number when multiplied together. In other words, we can say that if any number divides 60 ultimately, then it is the factor. Furthermore, we can derive the prime factors of 60 as it is a composite number. Apart from 60, more such numbers are composite in nature and have factors of more than 2, for example, 12, 18, 24, etc.

  • The factors of a number can be easily found through a simple multiplication technique. For example, the answer to the factors of 60 is relatively straightforward. It contains the multiplication of a pair of a number to get the result, in this case, 60. These pairs of numbers are called factors.

FAQs on Factors of 60

1. What is the main point to remember about factors of 60

The factors of 60 is probably the easiest chapter in the whole of mathematics. Like every other mathematical topic, the chapter of Factors of 60 depends on the multiplication methods. That is the only requirement to find the factors of 60. The multiplicational method is used so that the value, which is 60, can be found in the respective multiplication table. If any number is multiplied and can be the part of the multiplication when the answer is 60, then it is called a factor of 60. 

2. What is the result if there are no factors of 60?

Factors of 60, or any other number for that matter, has to be the factor in the answer 60 so that they can fall into the category. If there is a number which is divisible by any number (mainly 2, as it is the prime number) and does not have the answer as the one concerned – in this case, 60 – then it is not the factor of the concerned number and can be discarded from the calculation. It then does not get included in any of the further calculations. For example, the number 7 does not appear in any calculations as the factor of 60. 

3. What are the study tips for understanding of factors of 60

To study the topic of factors and factors of 60, students are highly recommended to go through the chapters of the subject, which can be easily accessed on our official site. Since the topic is mostly related to the numericals and practices rather than dealing with the theories, students are provided with content which is explained in the most simple and comprehensive language, along with the practice questions, which help the students gain better understanding of the concept as well as prepare them for the future examinations. 

4. How can I find the factors using prime numbers? 

The prime numbers are especially useful in finding the factors. In this case of a solution, which is regarding the factors of 60, we’ll have to take each number and see what is its divisibility. If the divisibility of a number falls under the criteria, then that basically is the factor. This can be done by individually bringing out all numbers and finding them against the number whose factor is being found and doing the LCM method. This can be explained in detail in the answer keys. 

5. What is the factor of 60 concept

To explain in simple words that are easier to understand, the number divides 60 evenly without having any remainder. So the number 60 is a composite number that has many divisors other than one and itself. It is also a positive integer obtained by the multiplication of two smaller positive integers. So the factors of 60 have no remainder left. And so, the factors of 60 are 12 and 5. This calculation can be applied to any number to find the solution.