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GCF of 56 and 96

GCF of 56 and 96 is the largest possible number that divides 56 and 96 exactly without any remainder. The factors of 56 and 96 are 1, 2, 4, 7, 8, 14, 28, 56 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 respectively. There are 3 commonly used methods to find the GCF of 56 and 96 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 56 and 96
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 56 and 96?

Answer: GCF of 56 and 96 is 8.

Explanation:

The GCF of two non-zero integers, x(56) and y(96), is the greatest positive integer m(8) that divides both x(56) and y(96) without any remainder.

Methods to Find GCF of 56 and 96

The methods to find the GCF of 56 and 96 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 56 and 96 by Listing Common Factors

Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

There are 4 common factors of 56 and 96, that are 8, 1, 2, and 4. Therefore, the greatest common factor of 56 and 96 is 8.

GCF of 56 and 96 by Prime Factorization

Prime factorization of 56 and 96 is (2 × 2 × 2 × 7) and (2 × 2 × 2 × 2 × 2 × 3) respectively. As visible, 56 and 96 have common prime factors. Hence, the GCF of 56 and 96 is 2 × 2 × 2 = 8.

GCF of 56 and 96 by Long Division

GCF of 56 and 96 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 96 (larger number) by 56 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (56) by the remainder (40).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (8) is the GCF of 56 and 96.

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GCF of 56 and 96 Examples

Example 1: Find the greatest number that divides 56 and 96 exactly.

Solution:

The greatest number that divides 56 and 96 exactly is their greatest common factor, i.e. GCF of 56 and 96.
⇒ Factors of 56 and 96:
- Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
- Factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Therefore, the GCF of 56 and 96 is 8.
Example 2: Find the GCF of 56 and 96, if their LCM is 672.

Solution:

∵ LCM × GCF = 56 × 96
⇒ GCF(56, 96) = (56 × 96)/672 = 8
Therefore, the greatest common factor of 56 and 96 is 8.
Example 3: For two numbers, GCF = 8 and LCM = 672. If one number is 56, find the other number.

Solution:

Given: GCF (z, 56) = 8 and LCM (z, 56) = 672
∵ GCF × LCM = 56 × (z)
⇒ z = (GCF × LCM)/56
⇒ z = (8 × 672)/56
⇒ z = 96
Therefore, the other number is 96.

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FAQs on GCF of 56 and 96

What is the GCF of 56 and 96?

The GCF of 56 and 96 is 8. To calculate the greatest common factor (GCF) of 56 and 96, we need to factor each number (factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56; factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96) and choose the greatest factor that exactly divides both 56 and 96, i.e., 8.

How to Find the GCF of 56 and 96 by Long Division Method?

To find the GCF of 56, 96 using long division method, 96 is divided by 56. The corresponding divisor (8) when remainder equals 0 is taken as GCF.

If the GCF of 96 and 56 is 8, Find its LCM.

GCF(96, 56) × LCM(96, 56) = 96 × 56
Since the GCF of 96 and 56 = 8
⇒ 8 × LCM(96, 56) = 5376
Therefore, LCM = 672
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 56, 96?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 56 and 96, i.e. GCF × LCM = 56 × 96.

What are the Methods to Find GCF of 56 and 96?

There are three commonly used methods to find the GCF of 56 and 96.

By Listing Common Factors
By Long Division
By Prime Factorization

How to Find the GCF of 56 and 96 by Prime Factorization?

To find the GCF of 56 and 96, we will find the prime factorization of the given numbers, i.e. 56 = 2 × 2 × 2 × 7; 96 = 2 × 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 56 and 96. Hence, GCF(56, 96) = 2 × 2 × 2 = 8
☛ What is a Prime Number?

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