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GCF of 12 and 48

GCF of 12 and 48 is the largest possible number that divides 12 and 48 exactly without any remainder. The factors of 12 and 48 are 1, 2, 3, 4, 6, 12 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 respectively. There are 3 commonly used methods to find the GCF of 12 and 48 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 12 and 48
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 12 and 48?

Answer: GCF of 12 and 48 is 12.

Explanation:

The GCF of two non-zero integers, x(12) and y(48), is the greatest positive integer m(12) that divides both x(12) and y(48) without any remainder.

Methods to Find GCF of 12 and 48

Let's look at the different methods for finding the GCF of 12 and 48.

Using Euclid's Algorithm
Listing Common Factors
Long Division Method

GCF of 12 and 48 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 = 48 and Y = 12

GCF(48, 12) = GCF(12, 48 mod 12) = GCF(12, 0)
GCF(12, 0) = 12 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 12 and 48 is 12.

GCF of 12 and 48 by Listing Common Factors

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

There are 6 common factors of 12 and 48, that are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor of 12 and 48 is 12.

GCF of 12 and 48 by Long Division

GCF of 12 and 48 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 48 (larger number) by 12 (smaller number).
Step 2: Since the remainder = 0, the divisor (12) is the GCF of 12 and 48.

The corresponding divisor (12) is the GCF of 12 and 48.

☛ Also Check:

GCF of 12 and 48 Examples

Example 1: The product of two numbers is 576. If their GCF is 12, what is their LCM?

Solution:

Given: GCF = 12 and product of numbers = 576
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 576/12
Therefore, the LCM is 48.
Example 2: For two numbers, GCF = 12 and LCM = 48. If one number is 12, find the other number.

Solution:

Given: GCF (y, 12) = 12 and LCM (y, 12) = 48
∵ GCF × LCM = 12 × (y)
⇒ y = (GCF × LCM)/12
⇒ y = (12 × 48)/12
⇒ y = 48
Therefore, the other number is 48.
Example 3: Find the GCF of 12 and 48, if their LCM is 48.

Solution:

∵ LCM × GCF = 12 × 48
⇒ GCF(12, 48) = (12 × 48)/48 = 12
Therefore, the greatest common factor of 12 and 48 is 12.

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FAQs on GCF of 12 and 48

What is the GCF of 12 and 48?

The GCF of 12 and 48 is 12. To calculate the greatest common factor (GCF) of 12 and 48, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48) and choose the greatest factor that exactly divides both 12 and 48, i.e., 12.

How to Find the GCF of 12 and 48 by Prime Factorization?

To find the GCF of 12 and 48, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 48 = 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 12 and 48. Hence, GCF(12, 48) = 2 × 2 × 3 = 12
☛ What is a Prime Number?

How to Find the GCF of 12 and 48 by Long Division Method?

To find the GCF of 12, 48 using long division method, 48 is divided by 12. The corresponding divisor (12) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 12, 48?

The following equation can be used to express the relation between LCM and GCF of 12 and 48, i.e. GCF × LCM = 12 × 48.

What are the Methods to Find GCF of 12 and 48?

There are three commonly used methods to find the GCF of 12 and 48.

By Listing Common Factors
By Prime Factorization
By Long Division

If the GCF of 48 and 12 is 12, Find its LCM.

GCF(48, 12) × LCM(48, 12) = 48 × 12
Since the GCF of 48 and 12 = 12
⇒ 12 × LCM(48, 12) = 576
Therefore, LCM = 48
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