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GCF of 15 and 57

GCF of 15 and 57 is the largest possible number that divides 15 and 57 exactly without any remainder. The factors of 15 and 57 are 1, 3, 5, 15 and 1, 3, 19, 57 respectively. There are 3 commonly used methods to find the GCF of 15 and 57 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 15 and 57
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 15 and 57?

Answer: GCF of 15 and 57 is 3.

Explanation:

The GCF of two non-zero integers, x(15) and y(57), is the greatest positive integer m(3) that divides both x(15) and y(57) without any remainder.

Methods to Find GCF of 15 and 57

The methods to find the GCF of 15 and 57 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 15 and 57 by Listing Common Factors

Factors of 15: 1, 3, 5, 15
Factors of 57: 1, 3, 19, 57

There are 2 common factors of 15 and 57, that are 1 and 3. Therefore, the greatest common factor of 15 and 57 is 3.

GCF of 15 and 57 by Prime Factorization

Prime factorization of 15 and 57 is (3 × 5) and (3 × 19) respectively. As visible, 15 and 57 have only one common prime factor i.e. 3. Hence, the GCF of 15 and 57 is 3.

GCF of 15 and 57 by Long Division

GCF of 15 and 57 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 57 (larger number) by 15 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (15) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 15 and 57.

☛ Also Check:

GCF of 15 and 57 Examples

Example 1: The product of two numbers is 855. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 855
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 855/3
Therefore, the LCM is 285.
Example 2: Find the GCF of 15 and 57, if their LCM is 285.

Solution:

∵ LCM × GCF = 15 × 57
⇒ GCF(15, 57) = (15 × 57)/285 = 3
Therefore, the greatest common factor of 15 and 57 is 3.
Example 3: For two numbers, GCF = 3 and LCM = 285. If one number is 15, find the other number.

Solution:

Given: GCF (z, 15) = 3 and LCM (z, 15) = 285
∵ GCF × LCM = 15 × (z)
⇒ z = (GCF × LCM)/15
⇒ z = (3 × 285)/15
⇒ z = 57
Therefore, the other number is 57.

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FAQs on GCF of 15 and 57

What is the GCF of 15 and 57?

The GCF of 15 and 57 is 3. To calculate the GCF (Greatest Common Factor) of 15 and 57, we need to factor each number (factors of 15 = 1, 3, 5, 15; factors of 57 = 1, 3, 19, 57) and choose the greatest factor that exactly divides both 15 and 57, i.e., 3.

If the GCF of 57 and 15 is 3, Find its LCM.

GCF(57, 15) × LCM(57, 15) = 57 × 15
Since the GCF of 57 and 15 = 3
⇒ 3 × LCM(57, 15) = 855
Therefore, LCM = 285
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 15 and 57?

There are three commonly used methods to find the GCF of 15 and 57.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the GCF of 15 and 57 by Prime Factorization?

To find the GCF of 15 and 57, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 57 = 3 × 19.
⇒ Since 3 is the only common prime factor of 15 and 57. Hence, GCF (15, 57) = 3.
☛ Prime Numbers

How to Find the GCF of 15 and 57 by Long Division Method?

To find the GCF of 15, 57 using long division method, 57 is divided by 15. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 15, 57?

The following equation can be used to express the relation between Least Common Multiple and GCF of 15 and 57, i.e. GCF × LCM = 15 × 57.

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