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GCF of 96 and 112

GCF of 96 and 112 is the largest possible number that divides 96 and 112 exactly without any remainder. The factors of 96 and 112 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 and 1, 2, 4, 7, 8, 14, 16, 28, 56, 112 respectively. There are 3 commonly used methods to find the GCF of 96 and 112 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 96 and 112
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 96 and 112?

Answer: GCF of 96 and 112 is 16.

Explanation:

The GCF of two non-zero integers, x(96) and y(112), is the greatest positive integer m(16) that divides both x(96) and y(112) without any remainder.

Methods to Find GCF of 96 and 112

The methods to find the GCF of 96 and 112 are explained below.

Long Division Method
Using Euclid's Algorithm
Prime Factorization Method

GCF of 96 and 112 by Long Division

GCF of 96 and 112 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 112 (larger number) by 96 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (96) by the remainder (16).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (16) is the GCF of 96 and 112.

GCF of 96 and 112 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 = 112 and Y = 96

GCF(112, 96) = GCF(96, 112 mod 96) = GCF(96, 16)
GCF(96, 16) = GCF(16, 96 mod 16) = GCF(16, 0)
GCF(16, 0) = 16 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 96 and 112 is 16.

GCF of 96 and 112 by Prime Factorization

Prime factorization of 96 and 112 is (2 × 2 × 2 × 2 × 2 × 3) and (2 × 2 × 2 × 2 × 7) respectively. As visible, 96 and 112 have common prime factors. Hence, the GCF of 96 and 112 is 2 × 2 × 2 × 2 = 16.

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GCF of 96 and 112 Examples

Example 1: The product of two numbers is 10752. If their GCF is 16, what is their LCM?

Solution:

Given: GCF = 16 and product of numbers = 10752
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 10752/16
Therefore, the LCM is 672.
Example 2: Find the greatest number that divides 96 and 112 exactly.

Solution:

The greatest number that divides 96 and 112 exactly is their greatest common factor, i.e. GCF of 96 and 112.
⇒ Factors of 96 and 112:
- Factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
- Factors of 112 = 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
Therefore, the GCF of 96 and 112 is 16.
Example 3: For two numbers, GCF = 16 and LCM = 672. If one number is 96, find the other number.

Solution:

Given: GCF (x, 96) = 16 and LCM (x, 96) = 672
∵ GCF × LCM = 96 × (x)
⇒ x = (GCF × LCM)/96
⇒ x = (16 × 672)/96
⇒ x = 112
Therefore, the other number is 112.

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FAQs on GCF of 96 and 112

What is the GCF of 96 and 112?

The GCF of 96 and 112 is 16. To calculate the greatest common factor (GCF) of 96 and 112, we need to factor each number (factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96; factors of 112 = 1, 2, 4, 7, 8, 14, 16, 28, 56, 112) and choose the greatest factor that exactly divides both 96 and 112, i.e., 16.

How to Find the GCF of 96 and 112 by Long Division Method?

To find the GCF of 96, 112 using long division method, 112 is divided by 96. The corresponding divisor (16) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 96, 112?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 96 and 112, i.e. GCF × LCM = 96 × 112.

How to Find the GCF of 96 and 112 by Prime Factorization?

To find the GCF of 96 and 112, we will find the prime factorization of the given numbers, i.e. 96 = 2 × 2 × 2 × 2 × 2 × 3; 112 = 2 × 2 × 2 × 2 × 7.
⇒ Since 2, 2, 2, 2 are common terms in the prime factorization of 96 and 112. Hence, GCF(96, 112) = 2 × 2 × 2 × 2 = 16
☛ Prime Number

What are the Methods to Find GCF of 96 and 112?

There are three commonly used methods to find the GCF of 96 and 112.

By Long Division
By Prime Factorization
By Listing Common Factors

If the GCF of 112 and 96 is 16, Find its LCM.

GCF(112, 96) × LCM(112, 96) = 112 × 96
Since the GCF of 112 and 96 = 16
⇒ 16 × LCM(112, 96) = 10752
Therefore, LCM = 672
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