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GCF of 38 and 95

GCF of 38 and 95 is the largest possible number that divides 38 and 95 exactly without any remainder. The factors of 38 and 95 are 1, 2, 19, 38 and 1, 5, 19, 95 respectively. There are 3 commonly used methods to find the GCF of 38 and 95 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 38 and 95
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 38 and 95?

Answer: GCF of 38 and 95 is 19.

Explanation:

The GCF of two non-zero integers, x(38) and y(95), is the greatest positive integer m(19) that divides both x(38) and y(95) without any remainder.

Methods to Find GCF of 38 and 95

The methods to find the GCF of 38 and 95 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 38 and 95 by Prime Factorization

Prime factorization of 38 and 95 is (2 × 19) and (5 × 19) respectively. As visible, 38 and 95 have only one common prime factor i.e. 19. Hence, the GCF of 38 and 95 is 19.

GCF of 38 and 95 by Long Division

GCF of 38 and 95 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 95 (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 95.

GCF of 38 and 95 by Listing Common Factors

Factors of 38: 1, 2, 19, 38
Factors of 95: 1, 5, 19, 95

There are 2 common factors of 38 and 95, that are 1 and 19. Therefore, the greatest common factor of 38 and 95 is 19.

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GCF of 38 and 95 Examples

Example 1: For two numbers, GCF = 19 and LCM = 190. If one number is 95, find the other number.

Solution:

Given: GCF (y, 95) = 19 and LCM (y, 95) = 190
∵ GCF × LCM = 95 × (y)
⇒ y = (GCF × LCM)/95
⇒ y = (19 × 190)/95
⇒ y = 38
Therefore, the other number is 38.
Example 2: The product of two numbers is 3610. If their GCF is 19, what is their LCM?

Solution:

Given: GCF = 19 and product of numbers = 3610
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 3610/19
Therefore, the LCM is 190.
Example 3: Find the greatest number that divides 38 and 95 exactly.

Solution:

The greatest number that divides 38 and 95 exactly is their greatest common factor, i.e. GCF of 38 and 95.
⇒ Factors of 38 and 95:
- Factors of 38 = 1, 2, 19, 38
- Factors of 95 = 1, 5, 19, 95
Therefore, the GCF of 38 and 95 is 19.

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FAQs on GCF of 38 and 95

What is the GCF of 38 and 95?

The GCF of 38 and 95 is 19. To calculate the greatest common factor of 38 and 95, we need to factor each number (factors of 38 = 1, 2, 19, 38; factors of 95 = 1, 5, 19, 95) and choose the greatest factor that exactly divides both 38 and 95, i.e., 19.

What are the Methods to Find GCF of 38 and 95?

There are three commonly used methods to find the GCF of 38 and 95.

By Euclidean Algorithm
By Prime Factorization
By Long Division

If the GCF of 95 and 38 is 19, Find its LCM.

GCF(95, 38) × LCM(95, 38) = 95 × 38
Since the GCF of 95 and 38 = 19
⇒ 19 × LCM(95, 38) = 3610
Therefore, LCM = 190
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How to Find the GCF of 38 and 95 by Long Division Method?

To find the GCF of 38, 95 using long division method, 95 is divided by 38. The corresponding divisor (19) when remainder equals 0 is taken as GCF.

How to Find the GCF of 38 and 95 by Prime Factorization?

To find the GCF of 38 and 95, we will find the prime factorization of the given numbers, i.e. 38 = 2 × 19; 95 = 5 × 19.
⇒ Since 19 is the only common prime factor of 38 and 95. Hence, GCF (38, 95) = 19.
☛ Prime Number

What is the Relation Between LCM and GCF of 38, 95?

The following equation can be used to express the relation between LCM and GCF of 38 and 95, i.e. GCF × LCM = 38 × 95.

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