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GCF of 38 and 57

GCF of 38 and 57 is the largest possible number that divides 38 and 57 exactly without any remainder. The factors of 38 and 57 are 1, 2, 19, 38 and 1, 3, 19, 57 respectively. There are 3 commonly used methods to find the GCF of 38 and 57 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 38 and 57
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 38 and 57?

Answer: GCF of 38 and 57 is 19.

Explanation:

The GCF of two non-zero integers, x(38) and y(57), is the greatest positive integer m(19) that divides both x(38) and y(57) without any remainder.

Methods to Find GCF of 38 and 57

The methods to find the GCF of 38 and 57 are explained below.

Using Euclid's Algorithm
Listing Common Factors
Long Division Method

GCF of 38 and 57 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 = 57 and Y = 38

GCF(57, 38) = GCF(38, 57 mod 38) = GCF(38, 19)
GCF(38, 19) = GCF(19, 38 mod 19) = GCF(19, 0)
GCF(19, 0) = 19 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 38 and 57 is 19.

GCF of 38 and 57 by Listing Common Factors

Factors of 38: 1, 2, 19, 38
Factors of 57: 1, 3, 19, 57

There are 2 common factors of 38 and 57, that are 1 and 19. Therefore, the greatest common factor of 38 and 57 is 19.

GCF of 38 and 57 by Long Division

GCF of 38 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 38 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (38) by the remainder (19).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (19) is the GCF of 38 and 57.

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GCF of 38 and 57 Examples

Example 1: The product of two numbers is 2166. If their GCF is 19, what is their LCM?

Solution:

Given: GCF = 19 and product of numbers = 2166
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2166/19
Therefore, the LCM is 114.
Example 2: Find the greatest number that divides 38 and 57 exactly.

Solution:

The greatest number that divides 38 and 57 exactly is their greatest common factor, i.e. GCF of 38 and 57.
⇒ Factors of 38 and 57:
- Factors of 38 = 1, 2, 19, 38
- Factors of 57 = 1, 3, 19, 57
Therefore, the GCF of 38 and 57 is 19.
Example 3: For two numbers, GCF = 19 and LCM = 114. If one number is 38, find the other number.

Solution:

Given: GCF (z, 38) = 19 and LCM (z, 38) = 114
∵ GCF × LCM = 38 × (z)
⇒ z = (GCF × LCM)/38
⇒ z = (19 × 114)/38
⇒ z = 57
Therefore, the other number is 57.

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FAQs on GCF of 38 and 57

What is the GCF of 38 and 57?

The GCF of 38 and 57 is 19. To calculate the greatest common factor (GCF) of 38 and 57, we need to factor each number (factors of 38 = 1, 2, 19, 38; factors of 57 = 1, 3, 19, 57) and choose the greatest factor that exactly divides both 38 and 57, i.e., 19.

What are the Methods to Find GCF of 38 and 57?

There are three commonly used methods to find the GCF of 38 and 57.

By Prime Factorization
By Long Division
By Euclidean Algorithm

If the GCF of 57 and 38 is 19, Find its LCM.

GCF(57, 38) × LCM(57, 38) = 57 × 38
Since the GCF of 57 and 38 = 19
⇒ 19 × LCM(57, 38) = 2166
Therefore, LCM = 114
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How to Find the GCF of 38 and 57 by Prime Factorization?

To find the GCF of 38 and 57, we will find the prime factorization of the given numbers, i.e. 38 = 2 × 19; 57 = 3 × 19.
⇒ Since 19 is the only common prime factor of 38 and 57. Hence, GCF (38, 57) = 19.
☛ What is a Prime Number?

How to Find the GCF of 38 and 57 by Long Division Method?

To find the GCF of 38, 57 using long division method, 57 is divided by 38. The corresponding divisor (19) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 38, 57?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 38 and 57, i.e. GCF × LCM = 38 × 57.

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