Factors of 60 are integers that can be divided evenly into 60. There are 12 factors of 60 of which 60 itself is the biggest factor and its prime factors are 2, 3 and 5 The sum of all factors of 60 is 168.

You are watching: What is the prime factorization of 60

Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60Negative Factors of 60: -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -30 and -60Prime Factors of 60: 2, 3, 5Prime Factorization of 60: 2 × 2 × 3 × 5 = 22 × 3 × 5Sum of Factors of 60: 168
1.What Are the Factors of 60?
2.How to Calculate Factors of 60?
3.Factors of 60 by Prime Factorization
4.Factors of 60 in Pairs
5.FAQs on Factors of 60

What are the Factors of 60?


The factors of 60 are all the numbers that give the value 60 when multiplied. As 60 is an even number, it has more than one factor. To understand why it is composite, let"s recall the definition of a composite number. A number is said to be composite if it has more than two factors.

60 ÷ 2 = 335 and 12 are factors of 60.Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

How to Calculate Factors of 60?

To calculate the factors of 60, we can use different methods like prime factorization and the division method. In prime factorization, we express 60 as a product of its prime factors and in the division method, we see what numbers divide 60 exactly. 

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

Explore factors using illustrations and interactive examples.

Factors of 60 by Prime Factorization

Prime factorization is the process of writing a number as a product of its prime factors. Let us learn how to find the factors of a number using prime factorization. We begin by searching for the smallest prime number which can divide 60 leaving the remainder as 0. As 60 is an even number, 2 is one of its factors.

Prime Factorization by Division

The number 60 is divided by the smallest prime number which divides 60 exactly, i.e. it leaves a remainder 0. The quotient is then divided by the smallest or second smallest prime number and the process continues till the quotient becomes indivisible. Let us divide 60 by the prime number 2⇒ 60 ÷ 2 = 30Now we need to divide the quotient 30 by the next least prime number. Since 30 is an even number, it is divisible by 2⇒ 30 ÷ 2 =1515 will be divisible by 3⇒ 15 ÷ 3= 55 is a prime number and hence not further divisible.

*

Prime factorization of 60 = 2 × 2 × 3 × 5Therefore, the prime factors of 60 are 2, 3, and 5.

Prime Factorization by Factor Tree

The other way of prime factorization is taking 60 as the root and creating branches by dividing it by the smallest prime number. This method is similar to the division method above. The difference lies in presenting the factorization. The figure below shows the factor tree of 60.

*

Collect all the numbers in circles and write 60 as the product of these numbers.Hence, 60 = 2 × 2 × 3 × 5


Pair factors are the factors of a number given in pairs, which when multiplied together, give that original number.6 and 10 both are factors of 60. For example, 6 × 10 = 60.The pair factors of 60 would be the two numbers which, when multiplied together, result in 60.

The following table represents the pair factors of 60:

ProductPair factors
1 × 60(1, 60)
2 × 30(2, 30)
3 × 20(3, 20)
4 × 15(4, 15)
5 × 12(5, 12)
6 × 10(6, 10)

We can have negative factors also for a given number. The negative pair factors of 60 are (-1, -60), (-2, -30), (-3, -20), (-4, -15), (-5, -12) and (-6, -10).

Important Notes:

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.Every even number will have 2 as one of its factors.60 is a composite number as it has more factors other than 1 and itself.

Challenging Questions:

What are the common factors of 60 and 600?Are 2/3 and 4/5 factors of 600?

Example 1: Fifteen friends have 60 pizzas from a pizza shop and distributed among themselves equally. How many pizzaz would each one of them get?

Solution:

15 pizzas are to be divided among friends equally.This implies we need to divide 60 by 15.60 ÷ 15 = 4Hence, each friend will get 4 pizzas.


Example 2: Sia wants to know if there are any common factors of 60 and 80. Help her in finding the answer to it.

Solution:

Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60Factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80The common factors of 60 and 80 = 1, 2, 4, 5, 10, and 20Hence, the common factors of 60 and 80 are 1, 2, 4, 5, 10, and 20.


Example 3: Find the product of all the prime factors of 60.

Solution:

Since, the prime factors of 60 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.


*


FAQs on Factors of 60

What are the Factors of 60?

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

What is the Greatest Common Factor of 60 and 21?

The factors of 60 and 21 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 and 1, 3, 7, 21 respectively.Common factors of 60 and 21 are <1, 3>.Hence, the GCF of 60 and 21 is 3.

What Numbers Are the Prime Factors of 60?

The prime factors of 60 are 2, 3, 5.

See more: It Is Nice To Meet You In Spanish, Nice To Meet You

What are the Common Factors of 60 and 38?

Since, the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 and the factors of 38 are 1, 2, 19, 38.Hence, <1, 2> are the common factors of 60 and 38.

What is the Sum of all the Factors of 60?

Sum of all factors of 60 = (22 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) = 168