Factors of 60

Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Factors of 60, is a set of numbers that perfectly divides 60. Factors of 60 are the numbers that divide 60 without leaving any remainder (i.e., with a remainder = 0).

In this article, we will learn about, Factors, Factors of 60 along with Prime Factorization and Factor Tree of 60.

What are Factors?

Factors are number that divides the given number evenly or perfectly i.e. Factors of a number completely divides that number without leaving any reminder behind.

Factors of a number can also be defined as the numbers which when multiplied in pairs returns the original number. Examples of Factors are:

• Factors of 15: 1, 3, 5 and 15.
• Factors of 18: 1, 2, 3, 6, 9, and 18.

Note : Every number has 1 and number itself as its factor.

What are Factors of 60?

Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20 ,30 and 60. Factors of 60 according to its definition are the numbers that can be multiplied with each other to give the product 60 as a result. Factors of 60 can be represented as:

• 1 × 60 = 60
• 2 × 30 = 60
• 3 × 20 = 60
• 4 × 15 = 60
• 5 × 12 = 60
• 6 × 10 = 60

Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Also, Each of this factor when divided by 60 leaves back the remainder as 0.

Read More, Factors of a number.

All Factors of 60

Here is a list of all the factors of 60:

Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Prime Factors of 60

Prime factors are prime numbers which when multiplied together gives back the original number. In simple words, prime factors are set of prime numbers which can divide it until the original number become 1.

Prime Factor of 60 are 2 , 3 and 5.

But we express it in given form:

Prime Factor of 60 are: 2² ,3 and 5 which are expressed as 2 ² × 3 × 5 = 60.

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• prime numbers 
• Whole number

How To Find Factors of 60?

In order to find the factors of 60, we need to identify all numbers that can divide 60 without leaving any remainder.

Here are steps we can follow:

• Strat from 1 till 60 and check if the number can divide 60 without leaving any reminder.

• If yes, then note down both the number and the result when 60 is divided by it.

• Else, check for next number and repeat it till number reaches 60.

• List all the Factors and the resulting list is 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

To check that all number obtained are satisfying the definition of factors that a factor can divide number without leaving any reminder:

Factors of 60	Division Equation	Reminder
1	60 ÷ 1 = 60	0
2	60 ÷ 2 = 30	0
3	60 ÷ 3 = 20	0
4	60 ÷ 4 = 15	0
5	60 ÷ 5 = 12	0
6	60 ÷ 6 = 10	0

The above table provides, the factors of 60 as 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Prime Factorization of 60

Prime Factorization is a method of obtaining factors of any number by dividing it with a prime number until the quotient changes to 1. Prime factorization is used to express a number as the product of its primes.

To find the prime factorization of 60, follow the given steps:

• Step 1: Choose smallest prime number(which is 2 here) which can perfectly divide 60 .

• Step 2: Divide 60 with the chosen number and note the result(30) and factor which is 2.

• Step 3: Repeat again same steps until the quotient turns to 1.

• Step 4: List all the numbers together to get all the prime factors of 60.

Below is the representation of Prime Factorization of 60.

Read more about Prime Factorization.

Factor Tree of 60

Factor Tree refers to the representation of a number as a product of its primes in the form of branches and leaves. A factor tree is a diagram that divides a number into its prime factors and represent it in a tree form.

The steps to draw prime factorization factor tree of 60 are as follows:

Step 1: Start with 60.

Step 2: Now find the smallest prime factor that divides 60. It’s 2 as shown in figure for first branch under 60.

Step 3: Continue dividing each branch by prime factors until you reach only prime numbers

Step 4: The prime factors are now at the ends of each branch. Arrange the list in ascending order, the prime factorization of 60 = 2 × 2 × 3 × 5.

Step 5: Exponents can be used to express repeated prime factors in form 2² × 3 × 5 for 60.

Here’s a factor tree for the number 60:

Factor Pairs of 60

As you might have noticed in above list of equation that result after dividing a number gives another factor. A factor pair of a number is the set of two of its factors, such that when multiplied gives number itself. In simple mathematics words, when we multiply two numbers we get a product. The factors of this product are the numbers that were multiplied to obtain it. Factor pairs refer to two numbers that, when multiplied together to gain a particular product.

As negative number when multiplied with another negative number it gives positive number so, here Negative numbers pairs can also be considered, So we can divide factor pairs on the basis of Positive factor pair and Negative factor pair.

Positive Factor Pairs of 60

Positive factor pairs of 60 are the pair of positive integer whose product gives 60 as a result.

Positive Factor Pair of 60	Multiplication of Factor Pair of 60
(1 , 60)	1 × 60 = 60
(2 , 30)	2 × 30 = 60
(3 , 20)	3 × 20 = 60
(4, 15)	4 × 15 = 60
(5 , 12)	5 × 12 = 60
(6 , 10)	6 × 10 = 60

Negative Factor Pairs of 60

Negative factor pairs of 60 are the pair of negative integer whose product gives 60(positive 60) as a result.

Negative Factor Pair of 60	Multiplication of Factor Pair of 60
(-1 , -60)	-1 × -60 = 60
(-2 , -30)	-2 × -30 = 60
(-3 , -20)	-3 × -20 = 60
(-4, -15)	-4 × -15 = 60
(-5 , -12)	-5 × -12 = 60
(-6 , -10)	-6 × -10 = 60

Read More,

• Factors of 12
• Factors of 36

Factors of 60 – Solved Examples

Example 1: What is the product of all the factors of 60?

Solution:

The factors of 60 are 1, 2, 3, 4, 6, 10, 12, 15 ,20, 30 and 60.

So, product =1 × 2 × 3 × 4 × 5 × 6 × 10 × 12 × 15 × 20 × 30 × 60. = 46656000000.

Example 2: What is the largest possible factor of 60 other than 60?

Solution:

30 is the largest possible factor of 60 other than 60.

Example 3: What are the prime factors of 60?

Solution:

Prime factor of 60 are 2² , 3 and 5.

Example 4: If d is a factor of both 60 and 15, what are the possible values of d?

Solution:

Factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15 ,20, 30 and 60.

Factors of 15 are: 1, 3, 5 and 15.

So possible values of d are: 1, 3, 5 and 15.

Example 5: What are the common factors of 60 and 45?

Solution:

Factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15 ,20, 30 and 60.

Factors of 45 are: 1, 3, 5, 9, 15, and 45.

Common Factors of 60 and 45 are : 1, 3, 5 and 15.

Factors of 60 – Practice Questions

Q1: Is (-2, -30) a negative factor pair of 60?

Q2: Write all factors of 60.

Q3: What is sum of all factors of 60?

Q4: Is 15 a factor of 60?

Q5: Is 60 itself a factor of 60?

Factor of 60: Frequently Asked Questions

What are the Factors of 60?

Factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15 ,20, 30 and 60.

Can Negative Numbers be Considered as Factors of 60?

Yes, negative numbers can be considered as Factors of 60.

What are the Possible Negative Factors of 60?

-1,- 2, -3,- 4,- 5,- 6, -10,-12, -15 ,-20, -30 and -60.

60 is Factor or Multiple of 60?

60 is both a factor and a multiple of 60.

Is 1 and Number itself a Factor of Every Number?

Yes , 1 and the number itself is always a factor of itself.