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GCF of 15 and 75

GCF of 15 and 75 is the largest possible number that divides 15 and 75 exactly without any remainder. The factors of 15 and 75 are 1, 3, 5, 15 and 1, 3, 5, 15, 25, 75 respectively. There are 3 commonly used methods to find the GCF of 15 and 75 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 15 and 75
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 15 and 75?

Answer: GCF of 15 and 75 is 15.

Explanation:

The GCF of two non-zero integers, x(15) and y(75), is the greatest positive integer m(15) that divides both x(15) and y(75) without any remainder.

Methods to Find GCF of 15 and 75

Let's look at the different methods for finding the GCF of 15 and 75.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 15 and 75 by Long Division

GCF of 15 and 75 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 75 (larger number) by 15 (smaller number).
Step 2: Since the remainder = 0, the divisor (15) is the GCF of 15 and 75.

The corresponding divisor (15) is the GCF of 15 and 75.

GCF of 15 and 75 by Listing Common Factors

Factors of 15: 1, 3, 5, 15
Factors of 75: 1, 3, 5, 15, 25, 75

There are 4 common factors of 15 and 75, that are 1, 3, 5, and 15. Therefore, the greatest common factor of 15 and 75 is 15.

GCF of 15 and 75 by Prime Factorization

Prime factorization of 15 and 75 is (3 × 5) and (3 × 5 × 5) respectively. As visible, 15 and 75 have common prime factors. Hence, the GCF of 15 and 75 is 3 × 5 = 15.

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GCF of 15 and 75 Examples

Example 1: Find the greatest number that divides 15 and 75 exactly.

Solution:

The greatest number that divides 15 and 75 exactly is their greatest common factor, i.e. GCF of 15 and 75.
⇒ Factors of 15 and 75:
- Factors of 15 = 1, 3, 5, 15
- Factors of 75 = 1, 3, 5, 15, 25, 75
Therefore, the GCF of 15 and 75 is 15.
Example 2: Find the GCF of 15 and 75, if their LCM is 75.

Solution:

∵ LCM × GCF = 15 × 75
⇒ GCF(15, 75) = (15 × 75)/75 = 15
Therefore, the greatest common factor of 15 and 75 is 15.
Example 3: The product of two numbers is 1125. If their GCF is 15, what is their LCM?

Solution:

Given: GCF = 15 and product of numbers = 1125
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1125/15
Therefore, the LCM is 75.

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FAQs on GCF of 15 and 75

What is the GCF of 15 and 75?

The GCF of 15 and 75 is 15. To calculate the greatest common factor (GCF) of 15 and 75, we need to factor each number (factors of 15 = 1, 3, 5, 15; factors of 75 = 1, 3, 5, 15, 25, 75) and choose the greatest factor that exactly divides both 15 and 75, i.e., 15.

How to Find the GCF of 15 and 75 by Long Division Method?

To find the GCF of 15, 75 using long division method, 75 is divided by 15. The corresponding divisor (15) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 15 and 75?

There are three commonly used methods to find the GCF of 15 and 75.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the GCF of 15 and 75 by Prime Factorization?

To find the GCF of 15 and 75, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 75 = 3 × 5 × 5.
⇒ Since 3, 5 are common terms in the prime factorization of 15 and 75. Hence, GCF(15, 75) = 3 × 5 = 15
☛ What are Prime Numbers?

What is the Relation Between LCM and GCF of 15, 75?

The following equation can be used to express the relation between Least Common Multiple and GCF of 15 and 75, i.e. GCF × LCM = 15 × 75.

If the GCF of 75 and 15 is 15, Find its LCM.

GCF(75, 15) × LCM(75, 15) = 75 × 15
Since the GCF of 75 and 15 = 15
⇒ 15 × LCM(75, 15) = 1125
Therefore, LCM = 75
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