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GCF of 15 and 48

GCF of 15 and 48 is the largest possible number that divides 15 and 48 exactly without any remainder. The factors of 15 and 48 are 1, 3, 5, 15 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 respectively. There are 3 commonly used methods to find the GCF of 15 and 48 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 15 and 48
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 15 and 48?

Answer: GCF of 15 and 48 is 3.

Explanation:

The GCF of two non-zero integers, x(15) and y(48), is the greatest positive integer m(3) that divides both x(15) and y(48) without any remainder.

Methods to Find GCF of 15 and 48

Let's look at the different methods for finding the GCF of 15 and 48.

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

GCF of 15 and 48 by Listing Common Factors

Factors of 15: 1, 3, 5, 15
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

There are 2 common factors of 15 and 48, that are 1 and 3. Therefore, the greatest common factor of 15 and 48 is 3.

GCF of 15 and 48 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 = 48 and Y = 15

GCF(48, 15) = GCF(15, 48 mod 15) = GCF(15, 3)
GCF(15, 3) = GCF(3, 15 mod 3) = GCF(3, 0)
GCF(3, 0) = 3 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 15 and 48 is 3.

GCF of 15 and 48 by Long Division

GCF of 15 and 48 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 48 (larger number) by 15 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (15) by the remainder (3).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 15 and 48.

☛ Also Check:

GCF of 15 and 48 Examples

Example 1: Find the GCF of 15 and 48, if their LCM is 240.

Solution:

∵ LCM × GCF = 15 × 48
⇒ GCF(15, 48) = (15 × 48)/240 = 3
Therefore, the greatest common factor of 15 and 48 is 3.
Example 2: Find the greatest number that divides 15 and 48 exactly.

Solution:

The greatest number that divides 15 and 48 exactly is their greatest common factor, i.e. GCF of 15 and 48.
⇒ Factors of 15 and 48:
- Factors of 15 = 1, 3, 5, 15
- Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Therefore, the GCF of 15 and 48 is 3.
Example 3: The product of two numbers is 720. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 720
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 720/3
Therefore, the LCM is 240.

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FAQs on GCF of 15 and 48

What is the GCF of 15 and 48?

The GCF of 15 and 48 is 3. To calculate the greatest common factor of 15 and 48, we need to factor each number (factors of 15 = 1, 3, 5, 15; factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48) and choose the greatest factor that exactly divides both 15 and 48, i.e., 3.

How to Find the GCF of 15 and 48 by Prime Factorization?

To find the GCF of 15 and 48, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 48 = 2 × 2 × 2 × 2 × 3.
⇒ Since 3 is the only common prime factor of 15 and 48. Hence, GCF (15, 48) = 3.
☛ What are Prime Numbers?

If the GCF of 48 and 15 is 3, Find its LCM.

GCF(48, 15) × LCM(48, 15) = 48 × 15
Since the GCF of 48 and 15 = 3
⇒ 3 × LCM(48, 15) = 720
Therefore, LCM = 240
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 15 and 48?

There are three commonly used methods to find the GCF of 15 and 48.

By Prime Factorization
By Long Division
By Euclidean Algorithm

How to Find the GCF of 15 and 48 by Long Division Method?

To find the GCF of 15, 48 using long division method, 48 is divided by 15. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 15, 48?

The following equation can be used to express the relation between Least Common Multiple and GCF of 15 and 48, i.e. GCF × LCM = 15 × 48.

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