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GCF of 36 and 48

GCF of 36 and 48 is the largest possible number that divides 36 and 48 exactly without any remainder. The factors of 36 and 48 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 respectively. There are 3 commonly used methods to find the GCF of 36 and 48 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 36 and 48
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 36 and 48?

Answer: GCF of 36 and 48 is 12.

Explanation:

The GCF of two non-zero integers, x(36) and y(48), is the greatest positive integer m(12) that divides both x(36) and y(48) without any remainder.

Methods to Find GCF of 36 and 48

The methods to find the GCF of 36 and 48 are explained below.

Using Euclid's Algorithm
Listing Common Factors
Prime Factorization Method

GCF of 36 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 = 36

GCF(48, 36) = GCF(36, 48 mod 36) = GCF(36, 12)
GCF(36, 12) = GCF(12, 36 mod 12) = GCF(12, 0)
GCF(12, 0) = 12 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 36 and 48 is 12.

GCF of 36 and 48 by Listing Common Factors

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

There are 6 common factors of 36 and 48, that are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor of 36 and 48 is 12.

GCF of 36 and 48 by Prime Factorization

Prime factorization of 36 and 48 is (2 × 2 × 3 × 3) and (2 × 2 × 2 × 2 × 3) respectively. As visible, 36 and 48 have common prime factors. Hence, the GCF of 36 and 48 is 2 × 2 × 3 = 12.

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GCF of 36 and 48 Examples

Example 1: The product of two numbers is 1728. If their GCF is 12, what is their LCM?

Solution:

Given: GCF = 12 and product of numbers = 1728
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1728/12
Therefore, the LCM is 144.
Example 2: For two numbers, GCF = 12 and LCM = 144. If one number is 36, find the other number.

Solution:

Given: GCF (y, 36) = 12 and LCM (y, 36) = 144
∵ GCF × LCM = 36 × (y)
⇒ y = (GCF × LCM)/36
⇒ y = (12 × 144)/36
⇒ y = 48
Therefore, the other number is 48.
Example 3: Find the GCF of 36 and 48, if their LCM is 144.

Solution:

∵ LCM × GCF = 36 × 48
⇒ GCF(36, 48) = (36 × 48)/144 = 12
Therefore, the greatest common factor of 36 and 48 is 12.

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FAQs on GCF of 36 and 48

What is the GCF of 36 and 48?

The GCF of 36 and 48 is 12. To calculate the GCF of 36 and 48, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48) and choose the greatest factor that exactly divides both 36 and 48, i.e., 12.

What is the Relation Between LCM and GCF of 36, 48?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 36 and 48, i.e. GCF × LCM = 36 × 48.

What are the Methods to Find GCF of 36 and 48?

There are three commonly used methods to find the GCF of 36 and 48.

By Prime Factorization
By Long Division
By Euclidean Algorithm

How to Find the GCF of 36 and 48 by Long Division Method?

To find the GCF of 36, 48 using long division method, 48 is divided by 36. The corresponding divisor (12) when remainder equals 0 is taken as GCF.

If the GCF of 48 and 36 is 12, Find its LCM.

GCF(48, 36) × LCM(48, 36) = 48 × 36
Since the GCF of 48 and 36 = 12
⇒ 12 × LCM(48, 36) = 1728
Therefore, LCM = 144
☛ Greatest Common Factor Calculator

How to Find the GCF of 36 and 48 by Prime Factorization?

To find the GCF of 36 and 48, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 48 = 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 36 and 48. Hence, GCF(36, 48) = 2 × 2 × 3 = 12
☛ What are Prime Numbers?

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