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GCF of 12 and 60

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

1.	GCF of 12 and 60
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 12 and 60?

Answer: GCF of 12 and 60 is 12.

Explanation:

The GCF of two non-zero integers, x(12) and y(60), is the greatest positive integer m(12) that divides both x(12) and y(60) without any remainder.

Methods to Find GCF of 12 and 60

The methods to find the GCF of 12 and 60 are explained below.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 12 and 60 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 60 and Y = 12

GCF(60, 12) = GCF(12, 60 mod 12) = GCF(12, 0)
GCF(12, 0) = 12 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 12 and 60 is 12.

GCF of 12 and 60 by Long Division

GCF of 12 and 60 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 60 (larger number) by 12 (smaller number).
Step 2: Since the remainder = 0, the divisor (12) is the GCF of 12 and 60.

The corresponding divisor (12) is the GCF of 12 and 60.

GCF of 12 and 60 by Listing Common Factors

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

There are 6 common factors of 12 and 60, that are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor of 12 and 60 is 12.

☛ Also Check:

GCF of 12 and 60 Examples

Example 1: The product of two numbers is 720. If their GCF is 12, what is their LCM?

Solution:

Given: GCF = 12 and product of numbers = 720
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 720/12
Therefore, the LCM is 60.
Example 2: Find the greatest number that divides 12 and 60 exactly.

Solution:

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

Solution:

Given: GCF (y, 60) = 12 and LCM (y, 60) = 60
∵ GCF × LCM = 60 × (y)
⇒ y = (GCF × LCM)/60
⇒ y = (12 × 60)/60
⇒ y = 12
Therefore, the other number is 12.

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FAQs on GCF of 12 and 60

What is the GCF of 12 and 60?

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

How to Find the GCF of 12 and 60 by Prime Factorization?

To find the GCF of 12 and 60, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 60 = 2 × 2 × 3 × 5.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 12 and 60. Hence, GCF(12, 60) = 2 × 2 × 3 = 12
☛ Prime Numbers

What is the Relation Between LCM and GCF of 12, 60?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 12 and 60, i.e. GCF × LCM = 12 × 60.

What are the Methods to Find GCF of 12 and 60?

There are three commonly used methods to find the GCF of 12 and 60.

By Prime Factorization
By Long Division
By Euclidean Algorithm

If the GCF of 60 and 12 is 12, Find its LCM.

GCF(60, 12) × LCM(60, 12) = 60 × 12
Since the GCF of 60 and 12 = 12
⇒ 12 × LCM(60, 12) = 720
Therefore, LCM = 60
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How to Find the GCF of 12 and 60 by Long Division Method?

To find the GCF of 12, 60 using long division method, 60 is divided by 12. The corresponding divisor (12) when remainder equals 0 is taken as GCF.

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