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GCF of 19 and 38

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

1.	GCF of 19 and 38
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 19 and 38?

Answer: GCF of 19 and 38 is 19.

Explanation:

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

Methods to Find GCF of 19 and 38

Let's look at the different methods for finding the GCF of 19 and 38.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

GCF of 19 and 38 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 = 38 and Y = 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 19 and 38 is 19.

GCF of 19 and 38 by Long Division

GCF of 19 and 38 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 38 (larger number) by 19 (smaller number).
Step 2: Since the remainder = 0, the divisor (19) is the GCF of 19 and 38.

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

GCF of 19 and 38 by Prime Factorization

Prime factorization of 19 and 38 is (19) and (2 × 19) respectively. As visible, 19 and 38 have only one common prime factor i.e. 19. Hence, the GCF of 19 and 38 is 19.

☛ Also Check:

GCF of 19 and 38 Examples

Example 1: The product of two numbers is 722. If their GCF is 19, what is their LCM?

Solution:

Given: GCF = 19 and product of numbers = 722
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 722/19
Therefore, the LCM is 38.
Example 2: Find the GCF of 19 and 38, if their LCM is 38.

Solution:

∵ LCM × GCF = 19 × 38
⇒ GCF(19, 38) = (19 × 38)/38 = 19
Therefore, the greatest common factor of 19 and 38 is 19.
Example 3: For two numbers, GCF = 19 and LCM = 38. If one number is 38, find the other number.

Solution:

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

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FAQs on GCF of 19 and 38

What is the GCF of 19 and 38?

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

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

GCF(38, 19) × LCM(38, 19) = 38 × 19
Since the GCF of 38 and 19 = 19
⇒ 19 × LCM(38, 19) = 722
Therefore, LCM = 38
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How to Find the GCF of 19 and 38 by Long Division Method?

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

How to Find the GCF of 19 and 38 by Prime Factorization?

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

What are the Methods to Find GCF of 19 and 38?

There are three commonly used methods to find the GCF of 19 and 38.

By Prime Factorization
By Listing Common Factors
By Long Division

What is the Relation Between LCM and GCF of 19, 38?

The following equation can be used to express the relation between LCM and GCF of 19 and 38, i.e. GCF × LCM = 19 × 38.

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