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

GCF of 28 and 32

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

1.	GCF of 28 and 32
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 28 and 32?

Answer: GCF of 28 and 32 is 4.

Explanation:

The GCF of two non-zero integers, x(28) and y(32), is the greatest positive integer m(4) that divides both x(28) and y(32) without any remainder.

Methods to Find GCF of 28 and 32

The methods to find the GCF of 28 and 32 are explained below.

Prime Factorization Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 28 and 32 by Prime Factorization

Prime factorization of 28 and 32 is (2 × 2 × 7) and (2 × 2 × 2 × 2 × 2) respectively. As visible, 28 and 32 have common prime factors. Hence, the GCF of 28 and 32 is 2 × 2 = 4.

GCF of 28 and 32 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 = 32 and Y = 28

GCF(32, 28) = GCF(28, 32 mod 28) = GCF(28, 4)
GCF(28, 4) = GCF(4, 28 mod 4) = GCF(4, 0)
GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 28 and 32 is 4.

GCF of 28 and 32 by Listing Common Factors

Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 32: 1, 2, 4, 8, 16, 32

There are 3 common factors of 28 and 32, that are 1, 2, and 4. Therefore, the greatest common factor of 28 and 32 is 4.

☛ Also Check:

GCF of 28 and 32 Examples

Example 1: Find the GCF of 28 and 32, if their LCM is 224.

Solution:

∵ LCM × GCF = 28 × 32
⇒ GCF(28, 32) = (28 × 32)/224 = 4
Therefore, the greatest common factor of 28 and 32 is 4.
Example 2: The product of two numbers is 896. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 896
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 896/4
Therefore, the LCM is 224.
Example 3: Find the greatest number that divides 28 and 32 exactly.

Solution:

The greatest number that divides 28 and 32 exactly is their greatest common factor, i.e. GCF of 28 and 32.
⇒ Factors of 28 and 32:
- Factors of 28 = 1, 2, 4, 7, 14, 28
- Factors of 32 = 1, 2, 4, 8, 16, 32
Therefore, the GCF of 28 and 32 is 4.

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 32

What is the GCF of 28 and 32?

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

What is the Relation Between LCM and GCF of 28, 32?

The following equation can be used to express the relation between Least Common Multiple and GCF of 28 and 32, i.e. GCF × LCM = 28 × 32.

If the GCF of 32 and 28 is 4, Find its LCM.

GCF(32, 28) × LCM(32, 28) = 32 × 28
Since the GCF of 32 and 28 = 4
⇒ 4 × LCM(32, 28) = 896
Therefore, LCM = 224
☛ GCF Calculator

How to Find the GCF of 28 and 32 by Long Division Method?

To find the GCF of 28, 32 using long division method, 32 is divided by 28. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 28 and 32?

There are three commonly used methods to find the GCF of 28 and 32.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the GCF of 28 and 32 by Prime Factorization?

To find the GCF of 28 and 32, we will find the prime factorization of the given numbers, i.e. 28 = 2 × 2 × 7; 32 = 2 × 2 × 2 × 2 × 2.
⇒ Since 2, 2 are common terms in the prime factorization of 28 and 32. Hence, GCF(28, 32) = 2 × 2 = 4
☛ What are Prime Numbers?

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum