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GCF of 15 and 24

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

1.	GCF of 15 and 24
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 15 and 24?

Answer: GCF of 15 and 24 is 3.

Explanation:

The GCF of two non-zero integers, x(15) and y(24), is the greatest positive integer m(3) that divides both x(15) and y(24) without any remainder.

Methods to Find GCF of 15 and 24

The methods to find the GCF of 15 and 24 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 15 and 24 by Prime Factorization

Prime factorization of 15 and 24 is (3 × 5) and (2 × 2 × 2 × 3) respectively. As visible, 15 and 24 have only one common prime factor i.e. 3. Hence, the GCF of 15 and 24 is 3.

GCF of 15 and 24 by Long Division

GCF of 15 and 24 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 24 (larger number) by 15 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (15) by the remainder (9).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 15 and 24.

GCF of 15 and 24 by Listing Common Factors

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

There are 2 common factors of 15 and 24, that are 1 and 3. Therefore, the greatest common factor of 15 and 24 is 3.

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GCF of 15 and 24 Examples

Example 1: Find the greatest number that divides 15 and 24 exactly.

Solution:

The greatest number that divides 15 and 24 exactly is their greatest common factor, i.e. GCF of 15 and 24.
⇒ Factors of 15 and 24:
- Factors of 15 = 1, 3, 5, 15
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
Therefore, the GCF of 15 and 24 is 3.
Example 2: The product of two numbers is 360. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 360
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 360/3
Therefore, the LCM is 120.
Example 3: For two numbers, GCF = 3 and LCM = 120. If one number is 15, find the other number.

Solution:

Given: GCF (x, 15) = 3 and LCM (x, 15) = 120
∵ GCF × LCM = 15 × (x)
⇒ x = (GCF × LCM)/15
⇒ x = (3 × 120)/15
⇒ x = 24
Therefore, the other number is 24.

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FAQs on GCF of 15 and 24

What is the GCF of 15 and 24?

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

What is the Relation Between LCM and GCF of 15, 24?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 15 and 24, i.e. GCF × LCM = 15 × 24.

What are the Methods to Find GCF of 15 and 24?

There are three commonly used methods to find the GCF of 15 and 24.

By Prime Factorization
By Euclidean Algorithm
By Long Division

How to Find the GCF of 15 and 24 by Prime Factorization?

To find the GCF of 15 and 24, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 24 = 2 × 2 × 2 × 3.
⇒ Since 3 is the only common prime factor of 15 and 24. Hence, GCF (15, 24) = 3.
☛ What are Prime Numbers?

How to Find the GCF of 15 and 24 by Long Division Method?

To find the GCF of 15, 24 using long division method, 24 is divided by 15. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

If the GCF of 24 and 15 is 3, Find its LCM.

GCF(24, 15) × LCM(24, 15) = 24 × 15
Since the GCF of 24 and 15 = 3
⇒ 3 × LCM(24, 15) = 360
Therefore, LCM = 120
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