A day full of math games & activities. Find one near you.

GCF of 28 and 98

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

1.	GCF of 28 and 98
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 28 and 98?

Answer: GCF of 28 and 98 is 14.

Explanation:

The GCF of two non-zero integers, x(28) and y(98), is the greatest positive integer m(14) that divides both x(28) and y(98) without any remainder.

Methods to Find GCF of 28 and 98

Let's look at the different methods for finding the GCF of 28 and 98.

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

GCF of 28 and 98 by Listing Common Factors

Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 98: 1, 2, 7, 14, 49, 98

There are 4 common factors of 28 and 98, that are 1, 2, 14, and 7. Therefore, the greatest common factor of 28 and 98 is 14.

GCF of 28 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 = 28

GCF(98, 28) = GCF(28, 98 mod 28) = GCF(28, 14)
GCF(28, 14) = GCF(14, 28 mod 14) = GCF(14, 0)
GCF(14, 0) = 14 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 28 and 98 is 14.

GCF of 28 and 98 by Long Division

GCF of 28 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 28 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (28) by the remainder (14).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (14) is the GCF of 28 and 98.

☛ Also Check:

GCF of 28 and 98 Examples

Example 1: For two numbers, GCF = 14 and LCM = 196. If one number is 28, find the other number.

Solution:

Given: GCF (y, 28) = 14 and LCM (y, 28) = 196
∵ GCF × LCM = 28 × (y)
⇒ y = (GCF × LCM)/28
⇒ y = (14 × 196)/28
⇒ y = 98
Therefore, the other number is 98.
Example 2: The product of two numbers is 2744. If their GCF is 14, what is their LCM?

Solution:

Given: GCF = 14 and product of numbers = 2744
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2744/14
Therefore, the LCM is 196.
Example 3: Find the GCF of 28 and 98, if their LCM is 196.

Solution:

∵ LCM × GCF = 28 × 98
⇒ GCF(28, 98) = (28 × 98)/196 = 14
Therefore, the greatest common factor of 28 and 98 is 14.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on GCF of 28 and 98

What is the GCF of 28 and 98?

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

How to Find the GCF of 28 and 98 by Prime Factorization?

To find the GCF of 28 and 98, we will find the prime factorization of the given numbers, i.e. 28 = 2 × 2 × 7; 98 = 2 × 7 × 7.
⇒ Since 2, 7 are common terms in the prime factorization of 28 and 98. Hence, GCF(28, 98) = 2 × 7 = 14
☛ Prime Number

What is the Relation Between LCM and GCF of 28, 98?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 28 and 98, i.e. GCF × LCM = 28 × 98.

What are the Methods to Find GCF of 28 and 98?

There are three commonly used methods to find the GCF of 28 and 98.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the GCF of 28 and 98 by Long Division Method?

To find the GCF of 28, 98 using long division method, 98 is divided by 28. The corresponding divisor (14) when remainder equals 0 is taken as GCF.

If the GCF of 98 and 28 is 14, Find its LCM.

GCF(98, 28) × LCM(98, 28) = 98 × 28
Since the GCF of 98 and 28 = 14
⇒ 14 × LCM(98, 28) = 2744
Therefore, LCM = 196
☛ GCF Calculator

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum