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GCF of 15 and 35

GCF of 15 and 35 is the largest possible number that divides 15 and 35 exactly without any remainder. The factors of 15 and 35 are 1, 3, 5, 15 and 1, 5, 7, 35 respectively. There are 3 commonly used methods to find the GCF of 15 and 35 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 15 and 35
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 15 and 35?

Answer: GCF of 15 and 35 is 5.

Explanation:

The GCF of two non-zero integers, x(15) and y(35), is the greatest positive integer m(5) that divides both x(15) and y(35) without any remainder.

Methods to Find GCF of 15 and 35

The methods to find the GCF of 15 and 35 are explained below.

Listing Common Factors
Using Euclid's Algorithm
Prime Factorization Method

GCF of 15 and 35 by Listing Common Factors

Factors of 15: 1, 3, 5, 15
Factors of 35: 1, 5, 7, 35

There are 2 common factors of 15 and 35, that are 1 and 5. Therefore, the greatest common factor of 15 and 35 is 5.

GCF of 15 and 35 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 = 35 and Y = 15

GCF(35, 15) = GCF(15, 35 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 35 is 5.

GCF of 15 and 35 by Prime Factorization

Prime factorization of 15 and 35 is (3 × 5) and (5 × 7) respectively. As visible, 15 and 35 have only one common prime factor i.e. 5. Hence, the GCF of 15 and 35 is 5.

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GCF of 15 and 35 Examples

Example 1: For two numbers, GCF = 5 and LCM = 105. If one number is 35, find the other number.

Solution:

Given: GCF (y, 35) = 5 and LCM (y, 35) = 105
∵ GCF × LCM = 35 × (y)
⇒ y = (GCF × LCM)/35
⇒ y = (5 × 105)/35
⇒ y = 15
Therefore, the other number is 15.
Example 2: The product of two numbers is 525. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 525
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 525/5
Therefore, the LCM is 105.
Example 3: Find the GCF of 15 and 35, if their LCM is 105.

Solution:

∵ LCM × GCF = 15 × 35
⇒ GCF(15, 35) = (15 × 35)/105 = 5
Therefore, the greatest common factor of 15 and 35 is 5.

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FAQs on GCF of 15 and 35

What is the GCF of 15 and 35?

The GCF of 15 and 35 is 5. To calculate the GCF of 15 and 35, we need to factor each number (factors of 15 = 1, 3, 5, 15; factors of 35 = 1, 5, 7, 35) and choose the greatest factor that exactly divides both 15 and 35, i.e., 5.

How to Find the GCF of 15 and 35 by Prime Factorization?

To find the GCF of 15 and 35, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 35 = 5 × 7.
⇒ Since 5 is the only common prime factor of 15 and 35. Hence, GCF (15, 35) = 5.
☛ What is a Prime Number?

What are the Methods to Find GCF of 15 and 35?

There are three commonly used methods to find the GCF of 15 and 35.

By Prime Factorization
By Long Division
By Euclidean Algorithm

If the GCF of 35 and 15 is 5, Find its LCM.

GCF(35, 15) × LCM(35, 15) = 35 × 15
Since the GCF of 35 and 15 = 5
⇒ 5 × LCM(35, 15) = 525
Therefore, LCM = 105
☛ Greatest Common Factor Calculator

How to Find the GCF of 15 and 35 by Long Division Method?

To find the GCF of 15, 35 using long division method, 35 is divided by 15. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 15, 35?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 15 and 35, i.e. GCF × LCM = 15 × 35.

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