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GCF of 24 and 32

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

1.	GCF of 24 and 32
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 24 and 32?

Answer: GCF of 24 and 32 is 8.

Explanation:

The GCF of two non-zero integers, x(24) and y(32), is the greatest positive integer m(8) that divides both x(24) and y(32) without any remainder.

Methods to Find GCF of 24 and 32

Let's look at the different methods for finding the GCF of 24 and 32.

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

GCF of 24 and 32 by Listing Common Factors

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

There are 4 common factors of 24 and 32, that are 8, 1, 2, and 4. Therefore, the greatest common factor of 24 and 32 is 8.

GCF of 24 and 32 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 = 32 and Y = 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 24 and 32 is 8.

GCF of 24 and 32 by Long Division

GCF of 24 and 32 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 32 (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 32.

☛ Also Check:

GCF of 24 and 32 Examples

Example 1: The product of two numbers is 768. If their GCF is 8, what is their LCM?

Solution:

Given: GCF = 8 and product of numbers = 768
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 768/8
Therefore, the LCM is 96.
Example 2: For two numbers, GCF = 8 and LCM = 96. If one number is 24, find the other number.

Solution:

Given: GCF (z, 24) = 8 and LCM (z, 24) = 96
∵ GCF × LCM = 24 × (z)
⇒ z = (GCF × LCM)/24
⇒ z = (8 × 96)/24
⇒ z = 32
Therefore, the other number is 32.
Example 3: Find the GCF of 24 and 32, if their LCM is 96.

Solution:

∵ LCM × GCF = 24 × 32
⇒ GCF(24, 32) = (24 × 32)/96 = 8
Therefore, the greatest common factor of 24 and 32 is 8.

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FAQs on GCF of 24 and 32

What is the GCF of 24 and 32?

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

If the GCF of 32 and 24 is 8, Find its LCM.

GCF(32, 24) × LCM(32, 24) = 32 × 24
Since the GCF of 32 and 24 = 8
⇒ 8 × LCM(32, 24) = 768
Therefore, LCM = 96
☛ GCF Calculator

How to Find the GCF of 24 and 32 by Prime Factorization?

To find the GCF of 24 and 32, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 32 = 2 × 2 × 2 × 2 × 2.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 24 and 32. Hence, GCF(24, 32) = 2 × 2 × 2 = 8
☛ Prime Number

How to Find the GCF of 24 and 32 by Long Division Method?

To find the GCF of 24, 32 using long division method, 32 is divided by 24. The corresponding divisor (8) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 24 and 32?

There are three commonly used methods to find the GCF of 24 and 32.

By Prime Factorization
By Listing Common Factors
By Long Division

What is the Relation Between LCM and GCF of 24, 32?

The following equation can be used to express the relation between Least Common Multiple and GCF of 24 and 32, i.e. GCF × LCM = 24 × 32.

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