GCF that 34 and also 38 is the largest possible number the divides 34 and also 38 exactly without any kind of remainder. The factors of 34 and also 38 room 1, 2, 17, 34 and also 1, 2, 19, 38 respectively. There room 3 generally used techniques to uncover the GCF the 34 and 38 - lengthy division, prime factorization, and also Euclidean algorithm.

You are watching: Greatest common factor of 34 and 38

1.GCF the 34 and 38
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF that 34 and 38 is 2.

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Explanation:

The GCF of 2 non-zero integers, x(34) and also y(38), is the greatest positive integer m(2) the divides both x(34) and y(38) without any remainder.


Let's look at the various methods because that finding the GCF the 34 and also 38.

Prime administer MethodListing common FactorsUsing Euclid's Algorithm

GCF of 34 and also 38 by element Factorization

Prime factorization of 34 and also 38 is (2 × 17) and also (2 × 19) respectively. As visible, 34 and also 38 have actually only one common prime factor i.e. 2. Hence, the GCF that 34 and 38 is 2.

GCF that 34 and also 38 by Listing common Factors

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Factors that 34: 1, 2, 17, 34Factors that 38: 1, 2, 19, 38

There are 2 typical factors the 34 and 38, that space 1 and also 2. Therefore, the greatest usual factor that 34 and 38 is 2.

GCF the 34 and 38 by Euclidean Algorithm

As every the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)where X > Y and mod is the modulo operator.

Here X = 38 and also Y = 34

GCF(38, 34) = GCF(34, 38 mode 34) = GCF(34, 4)GCF(34, 4) = GCF(4, 34 mod 4) = GCF(4, 2)GCF(4, 2) = GCF(2, 4 mode 2) = GCF(2, 0)GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF the 34 and 38 is 2.

☛ additionally Check:


GCF that 34 and 38 Examples


Example 1: find the greatest number the divides 34 and 38 exactly.

Solution:

The greatest number the divides 34 and also 38 precisely is your greatest common factor, i.e. GCF of 34 and also 38.⇒ components of 34 and also 38:

Factors of 34 = 1, 2, 17, 34Factors that 38 = 1, 2, 19, 38

Therefore, the GCF that 34 and also 38 is 2.


Example 2: For 2 numbers, GCF = 2 and also LCM = 646. If one number is 38, discover the other number.

Solution:

Given: GCF (x, 38) = 2 and LCM (x, 38) = 646∵ GCF × LCM = 38 × (x)⇒ x = (GCF × LCM)/38⇒ x = (2 × 646)/38⇒ x = 34Therefore, the other number is 34.


Example 3: find the GCF the 34 and also 38, if your LCM is 646.

Solution:

∵ LCM × GCF = 34 × 38⇒ GCF(34, 38) = (34 × 38)/646 = 2Therefore, the greatest usual factor the 34 and also 38 is 2.


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FAQs ~ above GCF that 34 and 38

What is the GCF that 34 and also 38?

The GCF of 34 and 38 is 2. To calculation the GCF the 34 and also 38, we need to variable each number (factors that 34 = 1, 2, 17, 34; factors of 38 = 1, 2, 19, 38) and choose the greatest element that specifically divides both 34 and 38, i.e., 2.

What are the methods to find GCF the 34 and also 38?

There space three typically used methods to discover the GCF the 34 and also 38.

By lengthy DivisionBy element FactorizationBy Listing common Factors

What is the Relation between LCM and also GCF of 34, 38?

The adhering to equation have the right to be supplied to refer the relation in between LCM (Least common Multiple) and GCF that 34 and 38, i.e. GCF × LCM = 34 × 38.

If the GCF the 38 and 34 is 2, find its LCM.

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GCF(38, 34) × LCM(38, 34) = 38 × 34Since the GCF of 38 and 34 = 2⇒ 2 × LCM(38, 34) = 1292Therefore, LCM = 646☛ Greatest typical Factor Calculator

How to uncover the GCF that 34 and also 38 by Long department Method?

To find the GCF that 34, 38 utilizing long division method, 38 is separated by 34. The corresponding divisor (2) once remainder equals 0 is taken as GCF.

How to discover the GCF the 34 and also 38 by prime Factorization?

To uncover the GCF that 34 and also 38, us will discover the prime factorization the the given numbers, i.e. 34 = 2 × 17; 38 = 2 × 19.⇒ because 2 is the only typical prime factor of 34 and also 38. Hence, GCF (34, 38) = 2.☛ element Number