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GCF of 24 and 45

GCF of 24 and 45 is the largest possible number that divides 24 and 45 exactly without any remainder. The factors of 24 and 45 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 3, 5, 9, 15, 45 respectively. There are 3 commonly used methods to find the GCF of 24 and 45 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 24 and 45
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 24 and 45?

Answer: GCF of 24 and 45 is 3.

Explanation:

The GCF of two non-zero integers, x(24) and y(45), is the greatest positive integer m(3) that divides both x(24) and y(45) without any remainder.

Methods to Find GCF of 24 and 45

Let's look at the different methods for finding the GCF of 24 and 45.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 24 and 45 by Long Division

GCF of 24 and 45 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 45 (larger number) by 24 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (24) by the remainder (21).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 24 and 45.

GCF of 24 and 45 by Listing Common Factors

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 45: 1, 3, 5, 9, 15, 45

There are 2 common factors of 24 and 45, that are 1 and 3. Therefore, the greatest common factor of 24 and 45 is 3.

GCF of 24 and 45 by Prime Factorization

Prime factorization of 24 and 45 is (2 × 2 × 2 × 3) and (3 × 3 × 5) respectively. As visible, 24 and 45 have only one common prime factor i.e. 3. Hence, the GCF of 24 and 45 is 3.

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GCF of 24 and 45 Examples

Example 1: For two numbers, GCF = 3 and LCM = 360. If one number is 24, find the other number.

Solution:

Given: GCF (y, 24) = 3 and LCM (y, 24) = 360
∵ GCF × LCM = 24 × (y)
⇒ y = (GCF × LCM)/24
⇒ y = (3 × 360)/24
⇒ y = 45
Therefore, the other number is 45.
Example 2: Find the GCF of 24 and 45, if their LCM is 360.

Solution:

∵ LCM × GCF = 24 × 45
⇒ GCF(24, 45) = (24 × 45)/360 = 3
Therefore, the greatest common factor of 24 and 45 is 3.
Example 3: The product of two numbers is 1080. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 1080
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1080/3
Therefore, the LCM is 360.

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FAQs on GCF of 24 and 45

What is the GCF of 24 and 45?

The GCF of 24 and 45 is 3. To calculate the GCF (Greatest Common Factor) of 24 and 45, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 45 = 1, 3, 5, 9, 15, 45) and choose the greatest factor that exactly divides both 24 and 45, i.e., 3.

What is the Relation Between LCM and GCF of 24, 45?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 24 and 45, i.e. GCF × LCM = 24 × 45.

How to Find the GCF of 24 and 45 by Prime Factorization?

To find the GCF of 24 and 45, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 45 = 3 × 3 × 5.
⇒ Since 3 is the only common prime factor of 24 and 45. Hence, GCF (24, 45) = 3.
☛ What are Prime Numbers?

How to Find the GCF of 24 and 45 by Long Division Method?

To find the GCF of 24, 45 using long division method, 45 is divided by 24. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 24 and 45?

There are three commonly used methods to find the GCF of 24 and 45.

By Prime Factorization
By Listing Common Factors
By Long Division

If the GCF of 45 and 24 is 3, Find its LCM.

GCF(45, 24) × LCM(45, 24) = 45 × 24
Since the GCF of 45 and 24 = 3
⇒ 3 × LCM(45, 24) = 1080
Therefore, LCM = 360
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