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GCF of 15 and 25

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

1.	GCF of 15 and 25
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 15 and 25?

Answer: GCF of 15 and 25 is 5.

Explanation:

The GCF of two non-zero integers, x(15) and y(25), is the greatest positive integer m(5) that divides both x(15) and y(25) without any remainder.

Methods to Find GCF of 15 and 25

The methods to find the GCF of 15 and 25 are explained below.

Using Euclid's Algorithm
Listing Common Factors
Prime Factorization Method

GCF of 15 and 25 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 = 25 and Y = 15

GCF(25, 15) = GCF(15, 25 mod 15) = GCF(15, 10)
GCF(15, 10) = GCF(10, 15 mod 10) = GCF(10, 5)
GCF(10, 5) = GCF(5, 10 mod 5) = GCF(5, 0)
GCF(5, 0) = 5 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 15 and 25 is 5.

GCF of 15 and 25 by Listing Common Factors

Factors of 15: 1, 3, 5, 15
Factors of 25: 1, 5, 25

There are 2 common factors of 15 and 25, that are 1 and 5. Therefore, the greatest common factor of 15 and 25 is 5.

GCF of 15 and 25 by Prime Factorization

Prime factorization of 15 and 25 is (3 × 5) and (5 × 5) respectively. As visible, 15 and 25 have only one common prime factor i.e. 5. Hence, the GCF of 15 and 25 is 5.

☛ Also Check:

GCF of 15 and 25 Examples

Example 1: The product of two numbers is 375. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 375
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 375/5
Therefore, the LCM is 75.
Example 2: For two numbers, GCF = 5 and LCM = 75. If one number is 15, find the other number.

Solution:

Given: GCF (y, 15) = 5 and LCM (y, 15) = 75
∵ GCF × LCM = 15 × (y)
⇒ y = (GCF × LCM)/15
⇒ y = (5 × 75)/15
⇒ y = 25
Therefore, the other number is 25.
Example 3: Find the GCF of 15 and 25, if their LCM is 75.

Solution:

∵ LCM × GCF = 15 × 25
⇒ GCF(15, 25) = (15 × 25)/75 = 5
Therefore, the greatest common factor of 15 and 25 is 5.

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FAQs on GCF of 15 and 25

What is the GCF of 15 and 25?

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

What is the Relation Between LCM and GCF of 15, 25?

The following equation can be used to express the relation between Least Common Multiple and GCF of 15 and 25, i.e. GCF × LCM = 15 × 25.

What are the Methods to Find GCF of 15 and 25?

There are three commonly used methods to find the GCF of 15 and 25.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 15 and 25 by Long Division Method?

To find the GCF of 15, 25 using long division method, 25 is divided by 15. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

How to Find the GCF of 15 and 25 by Prime Factorization?

To find the GCF of 15 and 25, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 25 = 5 × 5.
⇒ Since 5 is the only common prime factor of 15 and 25. Hence, GCF (15, 25) = 5.
☛ Prime Numbers

If the GCF of 25 and 15 is 5, Find its LCM.

GCF(25, 15) × LCM(25, 15) = 25 × 15
Since the GCF of 25 and 15 = 5
⇒ 5 × LCM(25, 15) = 375
Therefore, LCM = 75
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