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GCF of 60 and 20

GCF of 60 and 20 is the largest possible number that divides 60 and 20 exactly without any remainder. The factors of 60 and 20 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 and 1, 2, 4, 5, 10, 20 respectively. There are 3 commonly used methods to find the GCF of 60 and 20 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 60 and 20
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 60 and 20?

Answer: GCF of 60 and 20 is 20.

Explanation:

The GCF of two non-zero integers, x(60) and y(20), is the greatest positive integer m(20) that divides both x(60) and y(20) without any remainder.

Methods to Find GCF of 60 and 20

The methods to find the GCF of 60 and 20 are explained below.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 60 and 20 by Long Division

GCF of 60 and 20 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 60 (larger number) by 20 (smaller number).
Step 2: Since the remainder = 0, the divisor (20) is the GCF of 60 and 20.

The corresponding divisor (20) is the GCF of 60 and 20.

GCF of 60 and 20 by Listing Common Factors

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

There are 6 common factors of 60 and 20, that are 1, 2, 4, 5, 10, and 20. Therefore, the greatest common factor of 60 and 20 is 20.

GCF of 60 and 20 by Prime Factorization

Prime factorization of 60 and 20 is (2 × 2 × 3 × 5) and (2 × 2 × 5) respectively. As visible, 60 and 20 have common prime factors. Hence, the GCF of 60 and 20 is 2 × 2 × 5 = 20.

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GCF of 60 and 20 Examples

Example 1: Find the greatest number that divides 60 and 20 exactly.

Solution:

The greatest number that divides 60 and 20 exactly is their greatest common factor, i.e. GCF of 60 and 20.
⇒ Factors of 60 and 20:
- Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Factors of 20 = 1, 2, 4, 5, 10, 20
Therefore, the GCF of 60 and 20 is 20.
Example 2: The product of two numbers is 1200. If their GCF is 20, what is their LCM?

Solution:

Given: GCF = 20 and product of numbers = 1200
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1200/20
Therefore, the LCM is 60.
Example 3: For two numbers, GCF = 20 and LCM = 60. If one number is 20, find the other number.

Solution:

Given: GCF (z, 20) = 20 and LCM (z, 20) = 60
∵ GCF × LCM = 20 × (z)
⇒ z = (GCF × LCM)/20
⇒ z = (20 × 60)/20
⇒ z = 60
Therefore, the other number is 60.

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FAQs on GCF of 60 and 20

What is the GCF of 60 and 20?

The GCF of 60 and 20 is 20. To calculate the GCF of 60 and 20, we need to factor each number (factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60; factors of 20 = 1, 2, 4, 5, 10, 20) and choose the greatest factor that exactly divides both 60 and 20, i.e., 20.

If the GCF of 20 and 60 is 20, Find its LCM.

GCF(20, 60) × LCM(20, 60) = 20 × 60
Since the GCF of 20 and 60 = 20
⇒ 20 × LCM(20, 60) = 1200
Therefore, LCM = 60
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 60 and 20?

There are three commonly used methods to find the GCF of 60 and 20.

By Prime Factorization
By Listing Common Factors
By Long Division

How to Find the GCF of 60 and 20 by Prime Factorization?

To find the GCF of 60 and 20, we will find the prime factorization of the given numbers, i.e. 60 = 2 × 2 × 3 × 5; 20 = 2 × 2 × 5.
⇒ Since 2, 2, 5 are common terms in the prime factorization of 60 and 20. Hence, GCF(60, 20) = 2 × 2 × 5 = 20
☛ What is a Prime Number?

How to Find the GCF of 60 and 20 by Long Division Method?

To find the GCF of 60, 20 using long division method, 60 is divided by 20. The corresponding divisor (20) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 60, 20?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 60 and 20, i.e. GCF × LCM = 60 × 20.

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