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GCF of 28 and 35

GCF of 28 and 35 is the largest possible number that divides 28 and 35 exactly without any remainder. The factors of 28 and 35 are 1, 2, 4, 7, 14, 28 and 1, 5, 7, 35 respectively. There are 3 commonly used methods to find the GCF of 28 and 35 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 28 and 35
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 28 and 35?

Answer: GCF of 28 and 35 is 7

Explanation:

The GCF of two non-zero integers, x(28) and y(35), is the greatest positive integer m(7) that divides both x(28) and y(35) without any remainder.

Methods to Find GCF of 28 and 35

The methods to find the GCF of 28 and 35 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 28 and 35 by Long Division

GCF of 28 and 35 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 35 (larger number) by 28 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (28) by the remainder (7).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (7) is the GCF of 28 and 35.

GCF of 28 and 35 by Prime Factorization

Prime factorization of 28 and 35 is (2 × 2 × 7) and (5 × 7) respectively. As visible, 28 and 35 have only one common prime factor i.e. 7. Hence, the GCF of 28 and 35 is 7.

GCF of 28 and 35 by Listing Common Factors

Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 35: 1, 5, 7, 35

There are 2 common factors of 28 and 35, that are 1 and 7. Therefore, the greatest common factor of 28 and 35 is 7.

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GCF of 28 and 35 Examples

Example 1: The product of two numbers is 980. If their GCF is 7, what is their LCM?

Solution:

Given: GCF = 7 and product of numbers = 980
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 980/7
Therefore, the LCM is 140.
Example 2: For two numbers, GCF = 7 and LCM = 140. If one number is 28, find the other number.

Solution:

Given: GCF (z, 28) = 7 and LCM (z, 28) = 140
∵ GCF × LCM = 28 × (z)
⇒ z = (GCF × LCM)/28
⇒ z = (7 × 140)/28
⇒ z = 35
Therefore, the other number is 35.
Example 3: Find the GCF of 28 and 35, if their LCM is 140.

Solution:

∵ LCM × GCF = 28 × 35
⇒ GCF(28, 35) = (28 × 35)/140 = 7
Therefore, the greatest common factor of 28 and 35 is 7.

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FAQs on GCF of 28 and 35

What is the GCF of 28 and 35?

The GCF of 28 and 35 is 7. To calculate the GCF (Greatest Common Factor) of 28 and 35, we need to factor each number (factors of 28 = 1, 2, 4, 7, 14, 28; factors of 35 = 1, 5, 7, 35) and choose the greatest factor that exactly divides both 28 and 35, i.e., 7.

How to Find the GCF of 28 and 35 by Prime Factorization?

To find the GCF of 28 and 35, we will find the prime factorization of the given numbers, i.e. 28 = 2 × 2 × 7; 35 = 5 × 7.
⇒ Since 7 is the only common prime factor of 28 and 35. Hence, GCF (28, 35) = 7.
☛ Prime Number

If the GCF of 35 and 28 is 7, Find its LCM.

GCF(35, 28) × LCM(35, 28) = 35 × 28
Since the GCF of 35 and 28 = 7
⇒ 7 × LCM(35, 28) = 980
Therefore, LCM = 140
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 28 and 35?

There are three commonly used methods to find the GCF of 28 and 35.

By Prime Factorization
By Euclidean Algorithm
By Long Division

How to Find the GCF of 28 and 35 by Long Division Method?

To find the GCF of 28, 35 using long division method, 35 is divided by 28. The corresponding divisor (7) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 28, 35?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 28 and 35, i.e. GCF × LCM = 28 × 35.

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