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GCF of 48 and 64

GCF of 48 and 64 is the largest possible number that divides 48 and 64 exactly without any remainder. The factors of 48 and 64 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 and 1, 2, 4, 8, 16, 32, 64 respectively. There are 3 commonly used methods to find the GCF of 48 and 64 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 48 and 64
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 48 and 64?

Answer: GCF of 48 and 64 is 16.

Explanation:

The GCF of two non-zero integers, x(48) and y(64), is the greatest positive integer m(16) that divides both x(48) and y(64) without any remainder.

Methods to Find GCF of 48 and 64

The methods to find the GCF of 48 and 64 are explained below.

Listing Common Factors
Prime Factorization Method
Using Euclid's Algorithm

GCF of 48 and 64 by Listing Common Factors

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 64: 1, 2, 4, 8, 16, 32, 64

There are 5 common factors of 48 and 64, that are 1, 2, 4, 8, and 16. Therefore, the greatest common factor of 48 and 64 is 16.

GCF of 48 and 64 by Prime Factorization

Prime factorization of 48 and 64 is (2 × 2 × 2 × 2 × 3) and (2 × 2 × 2 × 2 × 2 × 2) respectively. As visible, 48 and 64 have common prime factors. Hence, the GCF of 48 and 64 is 2 × 2 × 2 × 2 = 16.

GCF of 48 and 64 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 = 64 and Y = 48

GCF(64, 48) = GCF(48, 64 mod 48) = GCF(48, 16)
GCF(48, 16) = GCF(16, 48 mod 16) = GCF(16, 0)
GCF(16, 0) = 16 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 48 and 64 is 16.

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GCF of 48 and 64 Examples

Example 1: For two numbers, GCF = 16 and LCM = 192. If one number is 48, find the other number.

Solution:

Given: GCF (z, 48) = 16 and LCM (z, 48) = 192
∵ GCF × LCM = 48 × (z)
⇒ z = (GCF × LCM)/48
⇒ z = (16 × 192)/48
⇒ z = 64
Therefore, the other number is 64.
Example 2: Find the GCF of 48 and 64, if their LCM is 192.

Solution:

∵ LCM × GCF = 48 × 64
⇒ GCF(48, 64) = (48 × 64)/192 = 16
Therefore, the greatest common factor of 48 and 64 is 16.
Example 3: The product of two numbers is 3072. If their GCF is 16, what is their LCM?

Solution:

Given: GCF = 16 and product of numbers = 3072
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 3072/16
Therefore, the LCM is 192.

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FAQs on GCF of 48 and 64

What is the GCF of 48 and 64?

The GCF of 48 and 64 is 16. To calculate the GCF of 48 and 64, we need to factor each number (factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48; factors of 64 = 1, 2, 4, 8, 16, 32, 64) and choose the greatest factor that exactly divides both 48 and 64, i.e., 16.

How to Find the GCF of 48 and 64 by Long Division Method?

To find the GCF of 48, 64 using long division method, 64 is divided by 48. The corresponding divisor (16) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 48, 64?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 48 and 64, i.e. GCF × LCM = 48 × 64.

What are the Methods to Find GCF of 48 and 64?

There are three commonly used methods to find the GCF of 48 and 64.

By Euclidean Algorithm
By Long Division
By Prime Factorization

If the GCF of 64 and 48 is 16, Find its LCM.

GCF(64, 48) × LCM(64, 48) = 64 × 48
Since the GCF of 64 and 48 = 16
⇒ 16 × LCM(64, 48) = 3072
Therefore, LCM = 192
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How to Find the GCF of 48 and 64 by Prime Factorization?

To find the GCF of 48 and 64, we will find the prime factorization of the given numbers, i.e. 48 = 2 × 2 × 2 × 2 × 3; 64 = 2 × 2 × 2 × 2 × 2 × 2.
⇒ Since 2, 2, 2, 2 are common terms in the prime factorization of 48 and 64. Hence, GCF(48, 64) = 2 × 2 × 2 × 2 = 16
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