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GCF of 28 and 64

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

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

What is GCF of 28 and 64?

Answer: GCF of 28 and 64 is 4.

Explanation:

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

Methods to Find GCF of 28 and 64

The methods to find the GCF of 28 and 64 are explained below.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 28 and 64 by Listing Common Factors

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

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

GCF of 28 and 64 by Long Division

GCF of 28 and 64 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 28 and 64.

GCF of 28 and 64 by Prime Factorization

Prime factorization of 28 and 64 is (2 × 2 × 7) and (2 × 2 × 2 × 2 × 2 × 2) respectively. As visible, 28 and 64 have common prime factors. Hence, the GCF of 28 and 64 is 2 × 2 = 4.

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GCF of 28 and 64 Examples

Example 1: Find the greatest number that divides 28 and 64 exactly.

Solution:

The greatest number that divides 28 and 64 exactly is their greatest common factor, i.e. GCF of 28 and 64.
⇒ Factors of 28 and 64:
- Factors of 28 = 1, 2, 4, 7, 14, 28
- Factors of 64 = 1, 2, 4, 8, 16, 32, 64
Therefore, the GCF of 28 and 64 is 4.
Example 2: The product of two numbers is 1792. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 1792
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1792/4
Therefore, the LCM is 448.
Example 3: For two numbers, GCF = 4 and LCM = 448. If one number is 64, find the other number.

Solution:

Given: GCF (z, 64) = 4 and LCM (z, 64) = 448
∵ GCF × LCM = 64 × (z)
⇒ z = (GCF × LCM)/64
⇒ z = (4 × 448)/64
⇒ z = 28
Therefore, the other number is 28.

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FAQs on GCF of 28 and 64

What is the GCF of 28 and 64?

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

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

GCF(64, 28) × LCM(64, 28) = 64 × 28
Since the GCF of 64 and 28 = 4
⇒ 4 × LCM(64, 28) = 1792
Therefore, LCM = 448
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How to Find the GCF of 28 and 64 by Long Division Method?

To find the GCF of 28, 64 using long division method, 64 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 64?

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

By Listing Common Factors
By Long Division
By Prime Factorization

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

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

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

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

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