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GCF of 24 and 56

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

1.	GCF of 24 and 56
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 24 and 56?

Answer: GCF of 24 and 56 is 8.

Explanation:

The GCF of two non-zero integers, x(24) and y(56), is the greatest positive integer m(8) that divides both x(24) and y(56) without any remainder.

Methods to Find GCF of 24 and 56

The methods to find the GCF of 24 and 56 are explained below.

Prime Factorization Method
Using Euclid's Algorithm
Long Division Method

GCF of 24 and 56 by Prime Factorization

Prime factorization of 24 and 56 is (2 × 2 × 2 × 3) and (2 × 2 × 2 × 7) respectively. As visible, 24 and 56 have common prime factors. Hence, the GCF of 24 and 56 is 2 × 2 × 2 = 8.

GCF of 24 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 = 24

GCF(56, 24) = GCF(24, 56 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 24 and 56 is 8.

GCF of 24 and 56 by Long Division

GCF of 24 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 24 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (24) by the remainder (8).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (8) is the GCF of 24 and 56.

☛ Also Check:

GCF of 24 and 56 Examples

Example 1: Find the greatest number that divides 24 and 56 exactly.

Solution:

The greatest number that divides 24 and 56 exactly is their greatest common factor, i.e. GCF of 24 and 56.
⇒ Factors of 24 and 56:
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
Therefore, the GCF of 24 and 56 is 8.
Example 2: For two numbers, GCF = 8 and LCM = 168. If one number is 24, find the other number.

Solution:

Given: GCF (z, 24) = 8 and LCM (z, 24) = 168
∵ GCF × LCM = 24 × (z)
⇒ z = (GCF × LCM)/24
⇒ z = (8 × 168)/24
⇒ z = 56
Therefore, the other number is 56.
Example 3: The product of two numbers is 1344. If their GCF is 8, what is their LCM?

Solution:

Given: GCF = 8 and product of numbers = 1344
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1344/8
Therefore, the LCM is 168.

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FAQs on GCF of 24 and 56

What is the GCF of 24 and 56?

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

What are the Methods to Find GCF of 24 and 56?

There are three commonly used methods to find the GCF of 24 and 56.

By Prime Factorization
By Long Division
By Listing Common Factors

What is the Relation Between LCM and GCF of 24, 56?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 24 and 56, i.e. GCF × LCM = 24 × 56.

How to Find the GCF of 24 and 56 by Prime Factorization?

To find the GCF of 24 and 56, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 56 = 2 × 2 × 2 × 7.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 24 and 56. Hence, GCF(24, 56) = 2 × 2 × 2 = 8
☛ What are Prime Numbers?

If the GCF of 56 and 24 is 8, Find its LCM.

GCF(56, 24) × LCM(56, 24) = 56 × 24
Since the GCF of 56 and 24 = 8
⇒ 8 × LCM(56, 24) = 1344
Therefore, LCM = 168
☛ GCF Calculator

How to Find the GCF of 24 and 56 by Long Division Method?

To find the GCF of 24, 56 using long division method, 56 is divided by 24. The corresponding divisor (8) when remainder equals 0 is taken as GCF.

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