Factors of 60

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 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:

Factor 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 with 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 number. 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. A factor tree resembles the following:

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.

FAQ (Frequently Asked Questions)

1. How Many Positive Factors of 60 are There?

Ans: The positive factors of 60 are a pair of a combination of two positive factors, that when multiplied together produces the number 60. The positive factors represent all those positive numbers that are divisible by 60. Here is the list of all positive factors pair of 60.

Positive Factor Pair of 60

1 × 60 = 60

2 × 30 = 60

3 × 20 = 60

4 × 15 = 60

5 × 12 = 60

6 × 10 = 60

10 × 6 = 60

12 × 5 = 60

15 × 4 = 60

20 × 3 = 60

30 × 2 = 60

60 × 1 = 60

2. Is 60 Prime or Composite?

Ans: First, we need to understand the basic difference between a prime number and a composite number. The prime number represents those numbers that are only divisible by 1 other than itself. While the composite numbers are those numbers that are evenly divided by more numbers other than itself and 1. 

So, based on the above definition we can easily say that 60 is a composite number that can be evenly divided by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, with no remainder. So, we can conclude that 60 is a composite number as it is divided by several numbers other than 1 and 60 itself.