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GCF of 48 and 96

GCF of 48 and 96 is the largest possible number that divides 48 and 96 exactly without any remainder. The factors of 48 and 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 respectively. There are 3 commonly used methods to find the GCF of 48 and 96 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 48 and 96
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 48 and 96?

Answer: GCF of 48 and 96 is 48.

Explanation:

The GCF of two non-zero integers, x(48) and y(96), is the greatest positive integer m(48) that divides both x(48) and y(96) without any remainder.

Methods to Find GCF of 48 and 96

Let's look at the different methods for finding the GCF of 48 and 96.

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

GCF of 48 and 96 by Listing Common Factors

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

There are 10 common factors of 48 and 96, that are 1, 2, 3, 4, 6, 8, 12, 16, 48, and 24. Therefore, the greatest common factor of 48 and 96 is 48.

GCF of 48 and 96 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 = 96 and Y = 48

GCF(96, 48) = GCF(48, 96 mod 48) = GCF(48, 0)
GCF(48, 0) = 48 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 48 and 96 is 48.

GCF of 48 and 96 by Long Division

GCF of 48 and 96 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 96 (larger number) by 48 (smaller number).
Step 2: Since the remainder = 0, the divisor (48) is the GCF of 48 and 96.

The corresponding divisor (48) is the GCF of 48 and 96.

☛ Also Check:

GCF of 48 and 96 Examples

Example 1: The product of two numbers is 4608. If their GCF is 48, what is their LCM?

Solution:

Given: GCF = 48 and product of numbers = 4608
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 4608/48
Therefore, the LCM is 96.
Example 2: Find the GCF of 48 and 96, if their LCM is 96.

Solution:

∵ LCM × GCF = 48 × 96
⇒ GCF(48, 96) = (48 × 96)/96 = 48
Therefore, the greatest common factor of 48 and 96 is 48.
Example 3: Find the greatest number that divides 48 and 96 exactly.

Solution:

The greatest number that divides 48 and 96 exactly is their greatest common factor, i.e. GCF of 48 and 96.
⇒ Factors of 48 and 96:
- Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Therefore, the GCF of 48 and 96 is 48.

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FAQs on GCF of 48 and 96

What is the GCF of 48 and 96?

The GCF of 48 and 96 is 48. To calculate the greatest common factor of 48 and 96, we need to factor each number (factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48; factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96) and choose the greatest factor that exactly divides both 48 and 96, i.e., 48.

How to Find the GCF of 48 and 96 by Prime Factorization?

To find the GCF of 48 and 96, we will find the prime factorization of the given numbers, i.e. 48 = 2 × 2 × 2 × 2 × 3; 96 = 2 × 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2, 2, 2, 3 are common terms in the prime factorization of 48 and 96. Hence, GCF(48, 96) = 2 × 2 × 2 × 2 × 3 = 48
☛ What are Prime Numbers?

If the GCF of 96 and 48 is 48, Find its LCM.

GCF(96, 48) × LCM(96, 48) = 96 × 48
Since the GCF of 96 and 48 = 48
⇒ 48 × LCM(96, 48) = 4608
Therefore, LCM = 96
☛ GCF Calculator

What is the Relation Between LCM and GCF of 48, 96?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 48 and 96, i.e. GCF × LCM = 48 × 96.

What are the Methods to Find GCF of 48 and 96?

There are three commonly used methods to find the GCF of 48 and 96.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the GCF of 48 and 96 by Long Division Method?

To find the GCF of 48, 96 using long division method, 96 is divided by 48. The corresponding divisor (48) when remainder equals 0 is taken as GCF.

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