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GCF of 24 and 30

GCF of 24 and 30 is the largest possible number that divides 24 and 30 exactly without any remainder. The factors of 24 and 30 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 3, 5, 6, 10, 15, 30 respectively. There are 3 commonly used methods to find the GCF of 24 and 30 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 24 and 30
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 24 and 30?

Answer: GCF of 24 and 30 is 6.

Explanation:

The GCF of two non-zero integers, x(24) and y(30), is the greatest positive integer m(6) that divides both x(24) and y(30) without any remainder.

Methods to Find GCF of 24 and 30

Let's look at the different methods for finding the GCF of 24 and 30.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

GCF of 24 and 30 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 = 30 and Y = 24

GCF(30, 24) = GCF(24, 30 mod 24) = GCF(24, 6)
GCF(24, 6) = GCF(6, 24 mod 6) = GCF(6, 0)
GCF(6, 0) = 6 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 24 and 30 is 6.

GCF of 24 and 30 by Long Division

GCF of 24 and 30 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 30 (larger number) by 24 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (24) by the remainder (6).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (6) is the GCF of 24 and 30.

GCF of 24 and 30 by Prime Factorization

Prime factorization of 24 and 30 is (2 × 2 × 2 × 3) and (2 × 3 × 5) respectively. As visible, 24 and 30 have common prime factors. Hence, the GCF of 24 and 30 is 2 × 3 = 6.

☛ Also Check:

GCF of 24 and 30 Examples

Example 1: For two numbers, GCF = 6 and LCM = 120. If one number is 30, find the other number.

Solution:

Given: GCF (z, 30) = 6 and LCM (z, 30) = 120
∵ GCF × LCM = 30 × (z)
⇒ z = (GCF × LCM)/30
⇒ z = (6 × 120)/30
⇒ z = 24
Therefore, the other number is 24.
Example 2: Find the GCF of 24 and 30, if their LCM is 120.

Solution:

∵ LCM × GCF = 24 × 30
⇒ GCF(24, 30) = (24 × 30)/120 = 6
Therefore, the greatest common factor of 24 and 30 is 6.
Example 3: The product of two numbers is 720. If their GCF is 6, what is their LCM?

Solution:

Given: GCF = 6 and product of numbers = 720
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 720/6
Therefore, the LCM is 120.

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FAQs on GCF of 24 and 30

What is the GCF of 24 and 30?

The GCF of 24 and 30 is 6. To calculate the GCF of 24 and 30, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30) and choose the greatest factor that exactly divides both 24 and 30, i.e., 6.

What are the Methods to Find GCF of 24 and 30?

There are three commonly used methods to find the GCF of 24 and 30.

By Long Division
By Prime Factorization
By Euclidean Algorithm

What is the Relation Between LCM and GCF of 24, 30?

The following equation can be used to express the relation between Least Common Multiple and GCF of 24 and 30, i.e. GCF × LCM = 24 × 30.

How to Find the GCF of 24 and 30 by Prime Factorization?

To find the GCF of 24 and 30, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 30 = 2 × 3 × 5.
⇒ Since 2, 3 are common terms in the prime factorization of 24 and 30. Hence, GCF(24, 30) = 2 × 3 = 6
☛ What is a Prime Number?

If the GCF of 30 and 24 is 6, Find its LCM.

GCF(30, 24) × LCM(30, 24) = 30 × 24
Since the GCF of 30 and 24 = 6
⇒ 6 × LCM(30, 24) = 720
Therefore, LCM = 120
☛ Greatest Common Factor Calculator

How to Find the GCF of 24 and 30 by Long Division Method?

To find the GCF of 24, 30 using long division method, 30 is divided by 24. The corresponding divisor (6) when remainder equals 0 is taken as GCF.

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