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GCF of 98 and 112

GCF of 98 and 112 is the largest possible number that divides 98 and 112 exactly without any remainder. The factors of 98 and 112 are 1, 2, 7, 14, 49, 98 and 1, 2, 4, 7, 8, 14, 16, 28, 56, 112 respectively. There are 3 commonly used methods to find the GCF of 98 and 112 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 98 and 112
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 98 and 112?

Answer: GCF of 98 and 112 is 14.

Explanation:

The GCF of two non-zero integers, x(98) and y(112), is the greatest positive integer m(14) that divides both x(98) and y(112) without any remainder.

Methods to Find GCF of 98 and 112

The methods to find the GCF of 98 and 112 are explained below.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 98 and 112 by Long Division

GCF of 98 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 98 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (98) by the remainder (14).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (14) is the GCF of 98 and 112.

GCF of 98 and 112 by Listing Common Factors

Factors of 98: 1, 2, 7, 14, 49, 98
Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112

There are 4 common factors of 98 and 112, which are 1, 2, 14, and 7. Therefore, the greatest common factor of 98 and 112 is 14.

GCF of 98 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 = 98

GCF(112, 98) = GCF(98, 112 mod 98) = GCF(98, 14)
GCF(98, 14) = GCF(14, 98 mod 14) = GCF(14, 0)
GCF(14, 0) = 14 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 98 and 112 is 14.

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GCF of 98 and 112 Examples

Example 1: For two numbers, GCF = 14 and LCM = 784. If one number is 112, find the other number.

Solution:

Given: GCF (z, 112) = 14 and LCM (z, 112) = 784
∵ GCF × LCM = 112 × (z)
⇒ z = (GCF × LCM)/112
⇒ z = (14 × 784)/112
⇒ z = 98
Therefore, the other number is 98.
Example 2: Find the greatest number that divides 98 and 112 exactly.

Solution:

The greatest number that divides 98 and 112 exactly is their greatest common factor, i.e. GCF of 98 and 112.
⇒ Factors of 98 and 112:
- Factors of 98 = 1, 2, 7, 14, 49, 98
- Factors of 112 = 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
Therefore, the GCF of 98 and 112 is 14.
Example 3: Find the GCF of 98 and 112, if their LCM is 784.

Solution:

∵ LCM × GCF = 98 × 112
⇒ GCF(98, 112) = (98 × 112)/784 = 14
Therefore, the greatest common factor of 98 and 112 is 14.

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FAQs on GCF of 98 and 112

What is the GCF of 98 and 112?

The GCF of 98 and 112 is 14. To calculate the greatest common factor of 98 and 112, we need to factor each number (factors of 98 = 1, 2, 7, 14, 49, 98; factors of 112 = 1, 2, 4, 7, 8, 14, 16, 28, 56, 112) and choose the greatest factor that exactly divides both 98 and 112, i.e., 14.

How to Find the GCF of 98 and 112 by Prime Factorization?

To find the GCF of 98 and 112, we will find the prime factorization of the given numbers, i.e. 98 = 2 × 7 × 7; 112 = 2 × 2 × 2 × 2 × 7.
⇒ Since 2, 7 are common terms in the prime factorization of 98 and 112. Hence, GCF(98, 112) = 2 × 7 = 14
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What is the Relation Between LCM and GCF of 98, 112?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 98 and 112, i.e. GCF × LCM = 98 × 112.

If the GCF of 112 and 98 is 14, Find its LCM.

GCF(112, 98) × LCM(112, 98) = 112 × 98
Since the GCF of 112 and 98 = 14
⇒ 14 × LCM(112, 98) = 10976
Therefore, LCM = 784
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How to Find the GCF of 98 and 112 by Long Division Method?

To find the GCF of 98, 112 using long division method, 112 is divided by 98. The corresponding divisor (14) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 98 and 112?

There are three commonly used methods to find the GCF of 98 and 112.

By Long Division
By Prime Factorization
By Listing Common Factors

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