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GCF of 56 and 64

GCF of 56 and 64 is the largest possible number that divides 56 and 64 exactly without any remainder. The factors of 56 and 64 are 1, 2, 4, 7, 8, 14, 28, 56 and 1, 2, 4, 8, 16, 32, 64 respectively. There are 3 commonly used methods to find the GCF of 56 and 64 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 56 and 64
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 56 and 64?

Answer: GCF of 56 and 64 is 8.

Explanation:

The GCF of two non-zero integers, x(56) and y(64), is the greatest positive integer m(8) that divides both x(56) and y(64) without any remainder.

Methods to Find GCF of 56 and 64

Let's look at the different methods for finding the GCF of 56 and 64.

Using Euclid's Algorithm
Prime Factorization Method
Listing Common Factors

GCF of 56 and 64 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 = 56

GCF(64, 56) = GCF(56, 64 mod 56) = GCF(56, 8)
GCF(56, 8) = GCF(8, 56 mod 8) = GCF(8, 0)
GCF(8, 0) = 8 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 56 and 64 is 8.

GCF of 56 and 64 by Prime Factorization

Prime factorization of 56 and 64 is (2 × 2 × 2 × 7) and (2 × 2 × 2 × 2 × 2 × 2) respectively. As visible, 56 and 64 have common prime factors. Hence, the GCF of 56 and 64 is 2 × 2 × 2 = 8.

GCF of 56 and 64 by Listing Common Factors

Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Factors of 64: 1, 2, 4, 8, 16, 32, 64

There are 4 common factors of 56 and 64, that are 8, 1, 2, and 4. Therefore, the greatest common factor of 56 and 64 is 8.

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GCF of 56 and 64 Examples

Example 1: Find the greatest number that divides 56 and 64 exactly.

Solution:

The greatest number that divides 56 and 64 exactly is their greatest common factor, i.e. GCF of 56 and 64.
⇒ Factors of 56 and 64:
- Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
- Factors of 64 = 1, 2, 4, 8, 16, 32, 64
Therefore, the GCF of 56 and 64 is 8.
Example 2: The product of two numbers is 3584. If their GCF is 8, what is their LCM?

Solution:

Given: GCF = 8 and product of numbers = 3584
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 3584/8
Therefore, the LCM is 448.
Example 3: Find the GCF of 56 and 64, if their LCM is 448.

Solution:

∵ LCM × GCF = 56 × 64
⇒ GCF(56, 64) = (56 × 64)/448 = 8
Therefore, the greatest common factor of 56 and 64 is 8.

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FAQs on GCF of 56 and 64

What is the GCF of 56 and 64?

The GCF of 56 and 64 is 8. To calculate the greatest common factor of 56 and 64, we need to factor each number (factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56; factors of 64 = 1, 2, 4, 8, 16, 32, 64) and choose the greatest factor that exactly divides both 56 and 64, i.e., 8.

How to Find the GCF of 56 and 64 by Long Division Method?

To find the GCF of 56, 64 using long division method, 64 is divided by 56. The corresponding divisor (8) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 56 and 64?

There are three commonly used methods to find the GCF of 56 and 64.

By Listing Common Factors
By Prime Factorization
By Long Division

What is the Relation Between LCM and GCF of 56, 64?

The following equation can be used to express the relation between Least Common Multiple and GCF of 56 and 64, i.e. GCF × LCM = 56 × 64.

If the GCF of 64 and 56 is 8, Find its LCM.

GCF(64, 56) × LCM(64, 56) = 64 × 56
Since the GCF of 64 and 56 = 8
⇒ 8 × LCM(64, 56) = 3584
Therefore, LCM = 448
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How to Find the GCF of 56 and 64 by Prime Factorization?

To find the GCF of 56 and 64, we will find the prime factorization of the given numbers, i.e. 56 = 2 × 2 × 2 × 7; 64 = 2 × 2 × 2 × 2 × 2 × 2.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 56 and 64. Hence, GCF(56, 64) = 2 × 2 × 2 = 8
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