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GCF of 15 and 50

GCF of 15 and 50 is the largest possible number that divides 15 and 50 exactly without any remainder. The factors of 15 and 50 are 1, 3, 5, 15 and 1, 2, 5, 10, 25, 50 respectively. There are 3 commonly used methods to find the GCF of 15 and 50 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 15 and 50
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 15 and 50?

Answer: GCF of 15 and 50 is 5.

Explanation:

The GCF of two non-zero integers, x(15) and y(50), is the greatest positive integer m(5) that divides both x(15) and y(50) without any remainder.

Methods to Find GCF of 15 and 50

Let's look at the different methods for finding the GCF of 15 and 50.

Listing Common Factors
Long Division Method
Using Euclid's Algorithm

GCF of 15 and 50 by Listing Common Factors

Factors of 15: 1, 3, 5, 15
Factors of 50: 1, 2, 5, 10, 25, 50

There are 2 common factors of 15 and 50, that are 1 and 5. Therefore, the greatest common factor of 15 and 50 is 5.

GCF of 15 and 50 by Long Division

GCF of 15 and 50 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 50 (larger number) by 15 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (15) by the remainder (5).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 15 and 50.

GCF of 15 and 50 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 = 50 and Y = 15

GCF(50, 15) = GCF(15, 50 mod 15) = GCF(15, 5)
GCF(15, 5) = GCF(5, 15 mod 5) = GCF(5, 0)
GCF(5, 0) = 5 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 15 and 50 is 5.

☛ Also Check:

GCF of 15 and 50 Examples

Example 1: Find the GCF of 15 and 50, if their LCM is 150.

Solution:

∵ LCM × GCF = 15 × 50
⇒ GCF(15, 50) = (15 × 50)/150 = 5
Therefore, the greatest common factor of 15 and 50 is 5.
Example 2: Find the greatest number that divides 15 and 50 exactly.

Solution:

The greatest number that divides 15 and 50 exactly is their greatest common factor, i.e. GCF of 15 and 50.
⇒ Factors of 15 and 50:
- Factors of 15 = 1, 3, 5, 15
- Factors of 50 = 1, 2, 5, 10, 25, 50
Therefore, the GCF of 15 and 50 is 5.
Example 3: The product of two numbers is 750. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 750
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 750/5
Therefore, the LCM is 150.

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FAQs on GCF of 15 and 50

What is the GCF of 15 and 50?

The GCF of 15 and 50 is 5. To calculate the greatest common factor of 15 and 50, we need to factor each number (factors of 15 = 1, 3, 5, 15; factors of 50 = 1, 2, 5, 10, 25, 50) and choose the greatest factor that exactly divides both 15 and 50, i.e., 5.

What are the Methods to Find GCF of 15 and 50?

There are three commonly used methods to find the GCF of 15 and 50.

By Long Division
By Prime Factorization
By Euclidean Algorithm

How to Find the GCF of 15 and 50 by Prime Factorization?

To find the GCF of 15 and 50, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 50 = 2 × 5 × 5.
⇒ Since 5 is the only common prime factor of 15 and 50. Hence, GCF (15, 50) = 5.
☛ What are Prime Numbers?

What is the Relation Between LCM and GCF of 15, 50?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 15 and 50, i.e. GCF × LCM = 15 × 50.

If the GCF of 50 and 15 is 5, Find its LCM.

GCF(50, 15) × LCM(50, 15) = 50 × 15
Since the GCF of 50 and 15 = 5
⇒ 5 × LCM(50, 15) = 750
Therefore, LCM = 150
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How to Find the GCF of 15 and 50 by Long Division Method?

To find the GCF of 15, 50 using long division method, 50 is divided by 15. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

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