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GCF of 96 and 120

GCF of 96 and 120 is the largest possible number that divides 96 and 120 exactly without any remainder. The factors of 96 and 120 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 respectively. There are 3 commonly used methods to find the GCF of 96 and 120 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 96 and 120
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 96 and 120?

Answer: GCF of 96 and 120 is 24.

Explanation:

The GCF of two non-zero integers, x(96) and y(120), is the greatest positive integer m(24) that divides both x(96) and y(120) without any remainder.

Methods to Find GCF of 96 and 120

Let's look at the different methods for finding the GCF of 96 and 120.

Using Euclid's Algorithm
Listing Common Factors
Long Division Method

GCF of 96 and 120 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 = 120 and Y = 96

GCF(120, 96) = GCF(96, 120 mod 96) = GCF(96, 24)
GCF(96, 24) = GCF(24, 96 mod 24) = GCF(24, 0)
GCF(24, 0) = 24 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 96 and 120 is 24.

GCF of 96 and 120 by Listing Common Factors

Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

There are 8 common factors of 96 and 120, that are 1, 2, 3, 4, 6, 8, 12, and 24. Therefore, the greatest common factor of 96 and 120 is 24.

GCF of 96 and 120 by Long Division

GCF of 96 and 120 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 120 (larger number) by 96 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (96) by the remainder (24).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (24) is the GCF of 96 and 120.

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GCF of 96 and 120 Examples

Example 1: For two numbers, GCF = 24 and LCM = 480. If one number is 96, find the other number.

Solution:

Given: GCF (y, 96) = 24 and LCM (y, 96) = 480
∵ GCF × LCM = 96 × (y)
⇒ y = (GCF × LCM)/96
⇒ y = (24 × 480)/96
⇒ y = 120
Therefore, the other number is 120.
Example 2: The product of two numbers is 11520. If their GCF is 24, what is their LCM?

Solution:

Given: GCF = 24 and product of numbers = 11520
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 11520/24
Therefore, the LCM is 480.
Example 3: Find the GCF of 96 and 120, if their LCM is 480.

Solution:

∵ LCM × GCF = 96 × 120
⇒ GCF(96, 120) = (96 × 120)/480 = 24
Therefore, the greatest common factor of 96 and 120 is 24.

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FAQs on GCF of 96 and 120

What is the GCF of 96 and 120?

The GCF of 96 and 120 is 24. To calculate the greatest common factor of 96 and 120, we need to factor each number (factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96; factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120) and choose the greatest factor that exactly divides both 96 and 120, i.e., 24.

How to Find the GCF of 96 and 120 by Prime Factorization?

To find the GCF of 96 and 120, we will find the prime factorization of the given numbers, i.e. 96 = 2 × 2 × 2 × 2 × 2 × 3; 120 = 2 × 2 × 2 × 3 × 5.
⇒ Since 2, 2, 2, 3 are common terms in the prime factorization of 96 and 120. Hence, GCF(96, 120) = 2 × 2 × 2 × 3 = 24
☛ What is a Prime Number?

What are the Methods to Find GCF of 96 and 120?

There are three commonly used methods to find the GCF of 96 and 120.

By Euclidean Algorithm
By Long Division
By Prime Factorization

What is the Relation Between LCM and GCF of 96, 120?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 96 and 120, i.e. GCF × LCM = 96 × 120.

How to Find the GCF of 96 and 120 by Long Division Method?

To find the GCF of 96, 120 using long division method, 120 is divided by 96. The corresponding divisor (24) when remainder equals 0 is taken as GCF.

If the GCF of 120 and 96 is 24, Find its LCM.

GCF(120, 96) × LCM(120, 96) = 120 × 96
Since the GCF of 120 and 96 = 24
⇒ 24 × LCM(120, 96) = 11520
Therefore, LCM = 480
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