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GCF of 49 and 98

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

1.	GCF of 49 and 98
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 49 and 98?

Answer: GCF of 49 and 98 is 49.

Explanation:

The GCF of two non-zero integers, x(49) and y(98), is the greatest positive integer m(49) that divides both x(49) and y(98) without any remainder.

Methods to Find GCF of 49 and 98

Let's look at the different methods for finding the GCF of 49 and 98.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 49 and 98 by Long Division

GCF of 49 and 98 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 98 (larger number) by 49 (smaller number).
Step 2: Since the remainder = 0, the divisor (49) is the GCF of 49 and 98.

The corresponding divisor (49) is the GCF of 49 and 98.

GCF of 49 and 98 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 = 98 and Y = 49

GCF(98, 49) = GCF(49, 98 mod 49) = GCF(49, 0)
GCF(49, 0) = 49 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 49 and 98 is 49.

GCF of 49 and 98 by Listing Common Factors

Factors of 49: 1, 7, 49
Factors of 98: 1, 2, 7, 14, 49, 98

There are 3 common factors of 49 and 98, that are 1, 7, and 49. Therefore, the greatest common factor of 49 and 98 is 49.

☛ Also Check:

GCF of 49 and 98 Examples

Example 1: Find the greatest number that divides 49 and 98 exactly.

Solution:

The greatest number that divides 49 and 98 exactly is their greatest common factor, i.e. GCF of 49 and 98.
⇒ Factors of 49 and 98:
- Factors of 49 = 1, 7, 49
- Factors of 98 = 1, 2, 7, 14, 49, 98
Therefore, the GCF of 49 and 98 is 49.
Example 2: The product of two numbers is 4802. If their GCF is 49, what is their LCM?

Solution:

Given: GCF = 49 and product of numbers = 4802
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 4802/49
Therefore, the LCM is 98.
Example 3: Find the GCF of 49 and 98, if their LCM is 98.

Solution:

∵ LCM × GCF = 49 × 98
⇒ GCF(49, 98) = (49 × 98)/98 = 49
Therefore, the greatest common factor of 49 and 98 is 49.

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FAQs on GCF of 49 and 98

What is the GCF of 49 and 98?

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

If the GCF of 98 and 49 is 49, Find its LCM.

GCF(98, 49) × LCM(98, 49) = 98 × 49
Since the GCF of 98 and 49 = 49
⇒ 49 × LCM(98, 49) = 4802
Therefore, LCM = 98
☛ GCF Calculator

How to Find the GCF of 49 and 98 by Prime Factorization?

To find the GCF of 49 and 98, we will find the prime factorization of the given numbers, i.e. 49 = 7 × 7; 98 = 2 × 7 × 7.
⇒ Since 7, 7 are common terms in the prime factorization of 49 and 98. Hence, GCF(49, 98) = 7 × 7 = 49
☛ Prime Numbers

What are the Methods to Find GCF of 49 and 98?

There are three commonly used methods to find the GCF of 49 and 98.

By Prime Factorization
By Euclidean Algorithm
By Long Division

How to Find the GCF of 49 and 98 by Long Division Method?

To find the GCF of 49, 98 using long division method, 98 is divided by 49. The corresponding divisor (49) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 49, 98?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 49 and 98, i.e. GCF × LCM = 49 × 98.

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