factor

# Factors of 60 | Prime Factorization of 60 | Factor Tree of 60

Written by Prerit Jain

Updated on: 18 Aug 2023

### Factors of 60 | Prime Factorization of 60 | Factor Tree of 60

Factors of 60: The numbers that divide 60 without leaving any remainder are called factors of 60.

There is a total of 12 factors for 60. Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

In this article, we have clearly explained three mathematical methods to find the factors of 60.

## What Are the Factors of 60?

Any two numbers that are multiplied together to give the result of the original product (60) are called factors of 60. In other words, the numbers that divide 60 exactly without leaving a remainder are called factors of 60. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. A number that has two or less than two factors is called a prime number. The numbers which have more than two factors are called composite numbers. Here, 60 has more than two factors, and hence 60 is a composite number.

## What Are the Factors of 60 in Pairs?

A set of two numbers multiplied together to get a particular product is known as a pair factor. For example, (30 x 2=60). So (30,2) is a pair factor in this case.

Similarly, a set of two numbers multiplied together to get the result of 60 is known as a pair factor of 60. Factors can be written in either positive or negative form.

### Positive Pair Factors of 60

Positive Pair factors of 60 are (1, 60), (2, 30), (3, 20), (4, 15), (5, 12), and (6, 10).

### Negative Pair Factors of 60

Negative Pair factors of 60 are (-1, -60), (-2, -30), (-3, -20), (-4, -15), (-5, -12), and (-6, -10).

### How To Find Factors of 60 by the Division Method?

A number(dividend) is divided by any number without leaving a remainder, then it is called as factor of 60 In this case, we divide 60 by using each of the integers to extract factors of 60. For your better understanding, we clearly explained the steps.

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 ÷ 35 = 2

60 ÷ 60 = 1

Hence, we can see that 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60 are the factors of 60.

### What Is the Prime Factorization of 60?

Prime factorization is one of the best mathematical method to find factors of 16. In this method, we have to check whether 60 is a prime number or a composite number as per the definition we came across above. Here, 60 is a composite number because it has more than two factors, so we are using the prime factorization method to find the factors of 60.

Step 1: First of all, we will take the smallest prime number 60 can be divided by and divide it. We will use 2 for this.
60 ÷ 2 = 30

Step 2: Now, we will see if 30 can be divided again by 2 or not at all.
30 ÷ 2 = 15

Step 3: Now, since we can see that 15 cannot be divided by 2 at all, we will use the next smallest prime number for dividing 15. We will use 3 for this.
15 ÷ 3 = 5

Step 4: As we can observe again, 5 is a prime number. So, that means it can only be divided by 5.
5 ÷ 5 = 1

At last, we can see that 1 is left and 1 cannot be divided by any number, so our prime factorization is complete. That means, Prime Factorization of 60 is 2 X 2 X 3 X 5 or 22 X 3 X 5. This also means that 2, 3, and 5 are the prime factors of 60.

### What is the Factor Tree of 60?

Students can also use the factor tree to find the prime factors of 60. In this method, we will place the number 60 at the top of the factor tree. Now, as part of the branches, we will write down any set of pair factors of the given number (60). Now, again, we will split the pair of factors into factors. This process will be continued until the branches become prime numbers. Now, circling all the prime numbers will give us the prime factors of 60.

Step 1: Let’s place the number 60 at the top of the factor tree and write down 150 in pairs, that is, 6 and 10.

Step 2: Since 6 is not a prime number, we will now divide 6 into 2 and 3.

Step 3: Since 2 and 3 are prime numbers, we can no longer separate them.

Step 4: As we can see, 10 is not a prime number, so we will split 10 into 2 and 5.

Step 5: We can see that 2 and 5 are both prime numbers. The branches in the factor tree will now be all the prime numbers.

Hence, circling all the branches, 22 X 3 X 5 or 2 X 2 X 3 X 5= 60, which are 60 prime factors.

There are many ways on which we can write the factor tree of 60. Below is an image representation of the factor tree of 60.

## Solved Examples on Factors of 60

What is the sum of all the factors of 60?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60 are the factors of 60.
1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 30 + 60 = 168
Hence, 168 is the sum of all factors of 60.

What’s the highest common factor between 60 and 30?
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
Hence, from the above, the common factors of 60 and 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
The highest common factor between 60 and 30 is 30.

What’s the highest common factor between 60 and 120?
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
Hence, from the above, the common factors of 60 and 120 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
The highest common factor between 60 and 120 is 60.

Is 15 a factor of 60?
Yes, 15 is a factor of 60.
As 60 ÷ 15 = 4.

Is 25 a factor of 60?
No, 25 is not a factor of 60.
As 60 ÷ 25 = Leaves a reminder.
Hence, 25 is not a factor of 60 since factors of a number (60) don’t leave a remainder after being divided.

What is the largest factor of 60?
The largest factor of 60 is 60.
The second largest factor of 60 is 30.

What are the first 5 factors of 60?
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
The first 5 factors of 60 are 1, 2, 3, 4, and 5.

## FAQs on Factors of 60

What are the factors and prime factors of 60?
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
The prime factors of 60 are: 2 X 2 X 3 X 5.

How many odd numbers are there in factors of 60?
A total of 4 odd numbers are there in factors of 60 and they are 1, 3, 5, and 15.

What are the factors of -60?
The factors of -60 are -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -30, and -60.

How many pair factors are there in 60?
A total of 6 pairs are there in factors of 60.

What are the factors of 60 in pairs?
(1, 60), (2, 30), (3, 20), (4, 15), (5, 12), and (6, 10) are the factors of 60 in pairs.

What are the composite numbers?
The numbers that have more than two factors are called composite numbers.

What are the positive factors for 60?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60 are the positive factors of 60.

That’s all for factors of 60 in this blog. We hope this has been helpful to you and easy to understand.

Written by by

Prerit Jain

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