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GCF of 24 and 64

GCF of 24 and 64 is the largest possible number that divides 24 and 64 exactly without any remainder. The factors of 24 and 64 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 4, 8, 16, 32, 64 respectively. There are 3 commonly used methods to find the GCF of 24 and 64 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 24 and 64
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 24 and 64?

Answer: GCF of 24 and 64 is 8.

Explanation:

The GCF of two non-zero integers, x(24) and y(64), is the greatest positive integer m(8) that divides both x(24) and y(64) without any remainder.

Methods to Find GCF of 24 and 64

Let's look at the different methods for finding the GCF of 24 and 64.

Listing Common Factors
Prime Factorization Method
Using Euclid's Algorithm

GCF of 24 and 64 by Listing Common Factors

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 64: 1, 2, 4, 8, 16, 32, 64

There are 4 common factors of 24 and 64, that are 8, 1, 2, and 4. Therefore, the greatest common factor of 24 and 64 is 8.

GCF of 24 and 64 by Prime Factorization

Prime factorization of 24 and 64 is (2 × 2 × 2 × 3) and (2 × 2 × 2 × 2 × 2 × 2) respectively. As visible, 24 and 64 have common prime factors. Hence, the GCF of 24 and 64 is 2 × 2 × 2 = 8.

GCF of 24 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 = 24

GCF(64, 24) = GCF(24, 64 mod 24) = GCF(24, 16)
GCF(24, 16) = GCF(16, 24 mod 16) = GCF(16, 8)
GCF(16, 8) = GCF(8, 16 mod 8) = GCF(8, 0)
GCF(8, 0) = 8 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 24 and 64 is 8.

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GCF of 24 and 64 Examples

Example 1: For two numbers, GCF = 8 and LCM = 192. If one number is 64, find the other number.

Solution:

Given: GCF (z, 64) = 8 and LCM (z, 64) = 192
∵ GCF × LCM = 64 × (z)
⇒ z = (GCF × LCM)/64
⇒ z = (8 × 192)/64
⇒ z = 24
Therefore, the other number is 24.
Example 2: Find the greatest number that divides 24 and 64 exactly.

Solution:

The greatest number that divides 24 and 64 exactly is their greatest common factor, i.e. GCF of 24 and 64.
⇒ Factors of 24 and 64:
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 64 = 1, 2, 4, 8, 16, 32, 64
Therefore, the GCF of 24 and 64 is 8.
Example 3: The product of two numbers is 1536. If their GCF is 8, what is their LCM?

Solution:

Given: GCF = 8 and product of numbers = 1536
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1536/8
Therefore, the LCM is 192.

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FAQs on GCF of 24 and 64

What is the GCF of 24 and 64?

The GCF of 24 and 64 is 8. To calculate the GCF (Greatest Common Factor) of 24 and 64, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 64 = 1, 2, 4, 8, 16, 32, 64) and choose the greatest factor that exactly divides both 24 and 64, i.e., 8.

How to Find the GCF of 24 and 64 by Long Division Method?

To find the GCF of 24, 64 using long division method, 64 is divided by 24. The corresponding divisor (8) when remainder equals 0 is taken as GCF.

How to Find the GCF of 24 and 64 by Prime Factorization?

To find the GCF of 24 and 64, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 64 = 2 × 2 × 2 × 2 × 2 × 2.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 24 and 64. Hence, GCF(24, 64) = 2 × 2 × 2 = 8
☛ What are Prime Numbers?

What are the Methods to Find GCF of 24 and 64?

There are three commonly used methods to find the GCF of 24 and 64.

By Listing Common Factors
By Prime Factorization
By Long Division

If the GCF of 64 and 24 is 8, Find its LCM.

GCF(64, 24) × LCM(64, 24) = 64 × 24
Since the GCF of 64 and 24 = 8
⇒ 8 × LCM(64, 24) = 1536
Therefore, LCM = 192
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What is the Relation Between LCM and GCF of 24, 64?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 24 and 64, i.e. GCF × LCM = 24 × 64.

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