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GCF of 96 and 144

GCF of 96 and 144 is the largest possible number that divides 96 and 144 exactly without any remainder. The factors of 96 and 144 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 and 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 respectively. There are 3 commonly used methods to find the GCF of 96 and 144 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 96 and 144
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 96 and 144?

Answer: GCF of 96 and 144 is 48.

Explanation:

The GCF of two non-zero integers, x(96) and y(144), is the greatest positive integer m(48) that divides both x(96) and y(144) without any remainder.

Methods to Find GCF of 96 and 144

Let's look at the different methods for finding the GCF of 96 and 144.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 96 and 144 by Long Division

GCF of 96 and 144 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 144 (larger number) by 96 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (96) by the remainder (48).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (48) is the GCF of 96 and 144.

GCF of 96 and 144 by Listing Common Factors

Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

There are 10 common factors of 96 and 144, that are 1, 2, 3, 4, 6, 8, 12, 16, 48, and 24. Therefore, the greatest common factor of 96 and 144 is 48.

GCF of 96 and 144 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 = 144 and Y = 96

GCF(144, 96) = GCF(96, 144 mod 96) = GCF(96, 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 96 and 144 is 48.

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GCF of 96 and 144 Examples

Example 1: Find the greatest number that divides 96 and 144 exactly.

Solution:

The greatest number that divides 96 and 144 exactly is their greatest common factor, i.e. GCF of 96 and 144.
⇒ Factors of 96 and 144:
- Factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
- Factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Therefore, the GCF of 96 and 144 is 48.
Example 2: The product of two numbers is 13824. If their GCF is 48, what is their LCM?

Solution:

Given: GCF = 48 and product of numbers = 13824
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 13824/48
Therefore, the LCM is 288.
Example 3: Find the GCF of 96 and 144, if their LCM is 288.

Solution:

∵ LCM × GCF = 96 × 144
⇒ GCF(96, 144) = (96 × 144)/288 = 48
Therefore, the greatest common factor of 96 and 144 is 48.

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FAQs on GCF of 96 and 144

What is the GCF of 96 and 144?

The GCF of 96 and 144 is 48. To calculate the greatest common factor of 96 and 144, we need to factor each number (factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96; factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144) and choose the greatest factor that exactly divides both 96 and 144, i.e., 48.

If the GCF of 144 and 96 is 48, Find its LCM.

GCF(144, 96) × LCM(144, 96) = 144 × 96
Since the GCF of 144 and 96 = 48
⇒ 48 × LCM(144, 96) = 13824
Therefore, LCM = 288
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 96, 144?

The following equation can be used to express the relation between LCM and GCF of 96 and 144, i.e. GCF × LCM = 96 × 144.

What are the Methods to Find GCF of 96 and 144?

There are three commonly used methods to find the GCF of 96 and 144.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 96 and 144 by Prime Factorization?

To find the GCF of 96 and 144, we will find the prime factorization of the given numbers, i.e. 96 = 2 × 2 × 2 × 2 × 2 × 3; 144 = 2 × 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 2, 2, 2, 3 are common terms in the prime factorization of 96 and 144. Hence, GCF(96, 144) = 2 × 2 × 2 × 2 × 3 = 48
☛ Prime Number

How to Find the GCF of 96 and 144 by Long Division Method?

To find the GCF of 96, 144 using long division method, 144 is divided by 96. The corresponding divisor (48) when remainder equals 0 is taken as GCF.

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