GCF of 15 and 30 is the largest possible number that divides 15 and 30 exactly without any remainder. The factors of 15 and 30 are 1, 3, 5, 15 and 1, 2, 3, 5, 6, 10, 15, 30 respectively. There are 3 commonly used methods to find the GCF of 15 and 30 - long division, prime factorization, and Euclidean algorithm.

You are watching: What is the greatest common factor of 15 and 30

1.GCF of 15 and 30
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF of 15 and 30 is 15.

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Explanation:

The GCF of two non-zero integers, x(15) and y(30), is the greatest positive integer m(15) that divides both x(15) and y(30) without any remainder.


The methods to find the GCF of 15 and 30 are explained below.

Prime Factorization MethodListing Common FactorsLong Division Method

GCF of 15 and 30 by Prime Factorization

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Prime factorization of 15 and 30 is (3 × 5) and (2 × 3 × 5) respectively. As visible, 15 and 30 have common prime factors. Hence, the GCF of 15 and 30 is 3 × 5 = 15.

GCF of 15 and 30 by Listing Common Factors

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Factors of 15: 1, 3, 5, 15Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

There are 4 common factors of 15 and 30, that are 1, 3, 5, and 15. Therefore, the greatest common factor of 15 and 30 is 15.

GCF of 15 and 30 by Long Division

GCF of 15 and 30 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 2: Since the remainder = 0, the divisor (15) is the GCF of 15 and 30.

The corresponding divisor (15) is the GCF of 15 and 30.

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GCF of 15 and 30 Examples


Example 1: For two numbers, GCF = 15 and LCM = 30. If one number is 30, find the other number.

Solution:

Given: GCF (y, 30) = 15 and LCM (y, 30) = 30∵ GCF × LCM = 30 × (y)⇒ y = (GCF × LCM)/30⇒ y = (15 × 30)/30⇒ y = 15Therefore, the other number is 15.


Example 2: Find the greatest number that divides 15 and 30 exactly.

Solution:

The greatest number that divides 15 and 30 exactly is their greatest common factor, i.e. GCF of 15 and 30.⇒ Factors of 15 and 30:

Factors of 15 = 1, 3, 5, 15Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30

Therefore, the GCF of 15 and 30 is 15.


Example 3: The product of two numbers is 450. If their GCF is 15, what is their LCM?

Solution:

Given: GCF = 15 and product of numbers = 450∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 450/15Therefore, the LCM is 30.


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FAQs on GCF of 15 and 30

What is the GCF of 15 and 30?

The GCF of 15 and 30 is 15. To calculate the GCF (Greatest Common Factor) of 15 and 30, we need to factor each number (factors of 15 = 1, 3, 5, 15; factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30) and choose the greatest factor that exactly divides both 15 and 30, i.e., 15.

If the GCF of 30 and 15 is 15, Find its LCM.

GCF(30, 15) × LCM(30, 15) = 30 × 15Since the GCF of 30 and 15 = 15⇒ 15 × LCM(30, 15) = 450Therefore, LCM = 30☛ Greatest Common Factor Calculator

How to Find the GCF of 15 and 30 by Prime Factorization?

To find the GCF of 15 and 30, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 30 = 2 × 3 × 5.⇒ Since 3, 5 are common terms in the prime factorization of 15 and 30. Hence, GCF(15, 30) = 3 × 5 = 15☛ What is a Prime Number?

How to Find the GCF of 15 and 30 by Long Division Method?

To find the GCF of 15, 30 using long division method, 30 is divided by 15. The corresponding divisor (15) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 15, 30?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 15 and 30, i.e. GCF × LCM = 15 × 30.

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What are the Methods to Find GCF of 15 and 30?

There are three commonly used methods to find the GCF of 15 and 30.