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GCF of 32 and 56

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

1.	GCF of 32 and 56
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 32 and 56?

Answer: GCF of 32 and 56 is 8.

Explanation:

The GCF of two non-zero integers, x(32) and y(56), is the greatest positive integer m(8) that divides both x(32) and y(56) without any remainder.

Methods to Find GCF of 32 and 56

Let's look at the different methods for finding the GCF of 32 and 56.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 32 and 56 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 = 56 and Y = 32

GCF(56, 32) = GCF(32, 56 mod 32) = GCF(32, 24)
GCF(32, 24) = GCF(24, 32 mod 24) = GCF(24, 8)
GCF(24, 8) = GCF(8, 24 mod 8) = GCF(8, 0)
GCF(8, 0) = 8 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 32 and 56 is 8.

GCF of 32 and 56 by Long Division

GCF of 32 and 56 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 56 (larger number) by 32 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (32) by the remainder (24).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (8) is the GCF of 32 and 56.

GCF of 32 and 56 by Listing Common Factors

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

There are 4 common factors of 32 and 56, that are 8, 1, 2, and 4. Therefore, the greatest common factor of 32 and 56 is 8.

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GCF of 32 and 56 Examples

Example 1: Find the GCF of 32 and 56, if their LCM is 224.

Solution:

∵ LCM × GCF = 32 × 56
⇒ GCF(32, 56) = (32 × 56)/224 = 8
Therefore, the greatest common factor of 32 and 56 is 8.
Example 2: Find the greatest number that divides 32 and 56 exactly.

Solution:

The greatest number that divides 32 and 56 exactly is their greatest common factor, i.e. GCF of 32 and 56.
⇒ Factors of 32 and 56:
- Factors of 32 = 1, 2, 4, 8, 16, 32
- Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
Therefore, the GCF of 32 and 56 is 8.
Example 3: The product of two numbers is 1792. If their GCF is 8, what is their LCM?

Solution:

Given: GCF = 8 and product of numbers = 1792
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1792/8
Therefore, the LCM is 224.

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FAQs on GCF of 32 and 56

What is the GCF of 32 and 56?

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

If the GCF of 56 and 32 is 8, Find its LCM.

GCF(56, 32) × LCM(56, 32) = 56 × 32
Since the GCF of 56 and 32 = 8
⇒ 8 × LCM(56, 32) = 1792
Therefore, LCM = 224
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What is the Relation Between LCM and GCF of 32, 56?

The following equation can be used to express the relation between Least Common Multiple and GCF of 32 and 56, i.e. GCF × LCM = 32 × 56.

How to Find the GCF of 32 and 56 by Long Division Method?

To find the GCF of 32, 56 using long division method, 56 is divided by 32. The corresponding divisor (8) when remainder equals 0 is taken as GCF.

How to Find the GCF of 32 and 56 by Prime Factorization?

To find the GCF of 32 and 56, we will find the prime factorization of the given numbers, i.e. 32 = 2 × 2 × 2 × 2 × 2; 56 = 2 × 2 × 2 × 7.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 32 and 56. Hence, GCF(32, 56) = 2 × 2 × 2 = 8
☛ What is a Prime Number?

What are the Methods to Find GCF of 32 and 56?

There are three commonly used methods to find the GCF of 32 and 56.

By Prime Factorization
By Listing Common Factors
By Long Division

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