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

GCF of 64 and 28

GCF of 64 and 28 is the largest possible number that divides 64 and 28 exactly without any remainder. The factors of 64 and 28 are 1, 2, 4, 8, 16, 32, 64 and 1, 2, 4, 7, 14, 28 respectively. There are 3 commonly used methods to find the GCF of 64 and 28 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 64 and 28
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 64 and 28?

Answer: GCF of 64 and 28 is 4.

Explanation:

The GCF of two non-zero integers, x(64) and y(28), is the greatest positive integer m(4) that divides both x(64) and y(28) without any remainder.

Methods to Find GCF of 64 and 28

Let's look at the different methods for finding the GCF of 64 and 28.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 64 and 28 by Long Division

GCF of 64 and 28 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 64 (larger number) by 28 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (28) by the remainder (8).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 64 and 28.

GCF of 64 and 28 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 = 64 and Y = 28

GCF(64, 28) = GCF(28, 64 mod 28) = GCF(28, 8)
GCF(28, 8) = GCF(8, 28 mod 8) = GCF(8, 4)
GCF(8, 4) = GCF(4, 8 mod 4) = GCF(4, 0)
GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 64 and 28 is 4.

GCF of 64 and 28 by Listing Common Factors

Factors of 64: 1, 2, 4, 8, 16, 32, 64
Factors of 28: 1, 2, 4, 7, 14, 28

There are 3 common factors of 64 and 28, that are 1, 2, and 4. Therefore, the greatest common factor of 64 and 28 is 4.

☛ Also Check:

GCF of 64 and 28 Examples

Example 1: For two numbers, GCF = 4 and LCM = 448. If one number is 28, find the other number.

Solution:

Given: GCF (x, 28) = 4 and LCM (x, 28) = 448
∵ GCF × LCM = 28 × (x)
⇒ x = (GCF × LCM)/28
⇒ x = (4 × 448)/28
⇒ x = 64
Therefore, the other number is 64.
Example 2: Find the greatest number that divides 64 and 28 exactly.

Solution:

The greatest number that divides 64 and 28 exactly is their greatest common factor, i.e. GCF of 64 and 28.
⇒ Factors of 64 and 28:
- Factors of 64 = 1, 2, 4, 8, 16, 32, 64
- Factors of 28 = 1, 2, 4, 7, 14, 28
Therefore, the GCF of 64 and 28 is 4.
Example 3: Find the GCF of 64 and 28, if their LCM is 448.

Solution:

∵ LCM × GCF = 64 × 28
⇒ GCF(64, 28) = (64 × 28)/448 = 4
Therefore, the greatest common factor of 64 and 28 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 64 and 28

What is the GCF of 64 and 28?

The GCF of 64 and 28 is 4. To calculate the GCF of 64 and 28, we need to factor each number (factors of 64 = 1, 2, 4, 8, 16, 32, 64; factors of 28 = 1, 2, 4, 7, 14, 28) and choose the greatest factor that exactly divides both 64 and 28, i.e., 4.

What is the Relation Between LCM and GCF of 64, 28?

The following equation can be used to express the relation between LCM and GCF of 64 and 28, i.e. GCF × LCM = 64 × 28.

How to Find the GCF of 64 and 28 by Prime Factorization?

To find the GCF of 64 and 28, we will find the prime factorization of the given numbers, i.e. 64 = 2 × 2 × 2 × 2 × 2 × 2; 28 = 2 × 2 × 7.
⇒ Since 2, 2 are common terms in the prime factorization of 64 and 28. Hence, GCF(64, 28) = 2 × 2 = 4
☛ Prime Number

What are the Methods to Find GCF of 64 and 28?

There are three commonly used methods to find the GCF of 64 and 28.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the GCF of 64 and 28 by Long Division Method?

To find the GCF of 64, 28 using long division method, 64 is divided by 28. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

If the GCF of 28 and 64 is 4, Find its LCM.

GCF(28, 64) × LCM(28, 64) = 28 × 64
Since the GCF of 28 and 64 = 4
⇒ 4 × LCM(28, 64) = 1792
Therefore, LCM = 448
☛ GCF Calculator

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum