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GCF of 108 and 24

GCF of 108 and 24 is the largest possible number that divides 108 and 24 exactly without any remainder. The factors of 108 and 24 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 and 1, 2, 3, 4, 6, 8, 12, 24 respectively. There are 3 commonly used methods to find the GCF of 108 and 24 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 108 and 24
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 108 and 24?

Answer: GCF of 108 and 24 is 12.

Explanation:

The GCF of two non-zero integers, x(108) and y(24), is the greatest positive integer m(12) that divides both x(108) and y(24) without any remainder.

Methods to Find GCF of 108 and 24

Let's look at the different methods for finding the GCF of 108 and 24.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

GCF of 108 and 24 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 = 108 and Y = 24

GCF(108, 24) = GCF(24, 108 mod 24) = GCF(24, 12)
GCF(24, 12) = GCF(12, 24 mod 12) = GCF(12, 0)
GCF(12, 0) = 12 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 108 and 24 is 12.

GCF of 108 and 24 by Prime Factorization

Prime factorization of 108 and 24 is (2 × 2 × 3 × 3 × 3) and (2 × 2 × 2 × 3) respectively. As visible, 108 and 24 have common prime factors. Hence, the GCF of 108 and 24 is 2 × 2 × 3 = 12.

GCF of 108 and 24 by Long Division

GCF of 108 and 24 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 108 (larger number) by 24 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (24) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (12) is the GCF of 108 and 24.

☛ Also Check:

GCF of 108 and 24 Examples

Example 1: Find the GCF of 108 and 24, if their LCM is 216.

Solution:

∵ LCM × GCF = 108 × 24
⇒ GCF(108, 24) = (108 × 24)/216 = 12
Therefore, the greatest common factor of 108 and 24 is 12.
Example 2: For two numbers, GCF = 12 and LCM = 216. If one number is 24, find the other number.

Solution:

Given: GCF (z, 24) = 12 and LCM (z, 24) = 216
∵ GCF × LCM = 24 × (z)
⇒ z = (GCF × LCM)/24
⇒ z = (12 × 216)/24
⇒ z = 108
Therefore, the other number is 108.
Example 3: Find the greatest number that divides 108 and 24 exactly.

Solution:

The greatest number that divides 108 and 24 exactly is their greatest common factor, i.e. GCF of 108 and 24.
⇒ Factors of 108 and 24:
- Factors of 108 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
Therefore, the GCF of 108 and 24 is 12.

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FAQs on GCF of 108 and 24

What is the GCF of 108 and 24?

The GCF of 108 and 24 is 12. To calculate the GCF (Greatest Common Factor) of 108 and 24, we need to factor each number (factors of 108 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108; factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24) and choose the greatest factor that exactly divides both 108 and 24, i.e., 12.

How to Find the GCF of 108 and 24 by Long Division Method?

To find the GCF of 108, 24 using long division method, 108 is divided by 24. The corresponding divisor (12) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 108 and 24?

There are three commonly used methods to find the GCF of 108 and 24.

By Listing Common Factors
By Prime Factorization
By Long Division

What is the Relation Between LCM and GCF of 108, 24?

The following equation can be used to express the relation between LCM and GCF of 108 and 24, i.e. GCF × LCM = 108 × 24.

If the GCF of 24 and 108 is 12, Find its LCM.

GCF(24, 108) × LCM(24, 108) = 24 × 108
Since the GCF of 24 and 108 = 12
⇒ 12 × LCM(24, 108) = 2592
Therefore, LCM = 216
☛ Greatest Common Factor Calculator

How to Find the GCF of 108 and 24 by Prime Factorization?

To find the GCF of 108 and 24, we will find the prime factorization of the given numbers, i.e. 108 = 2 × 2 × 3 × 3 × 3; 24 = 2 × 2 × 2 × 3.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 108 and 24. Hence, GCF(108, 24) = 2 × 2 × 3 = 12
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