GCF of 30 and 75 is the largest possible number the divides 30 and also 75 exactly without any type of remainder. The determinants of 30 and 75 space 1, 2, 3, 5, 6, 10, 15, 30 and 1, 3, 5, 15, 25, 75 respectively. There are 3 commonly used techniques to uncover the GCF the 30 and 75 - lengthy division, Euclidean algorithm, and prime factorization.

You are watching: What is the greatest common factor of 30 and 75

1.GCF that 30 and 75
2.List the Methods
3.Solved Examples
4.FAQs

Answer: GCF of 30 and also 75 is 15.

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Explanation:

The GCF of two non-zero integers, x(30) and y(75), is the biggest positive essence m(15) the divides both x(30) and y(75) without any remainder.


The approaches to discover the GCF the 30 and 75 are defined below.

Listing typical FactorsUsing Euclid's AlgorithmPrime administer Method

GCF the 30 and 75 through Listing typical Factors

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Factors that 30: 1, 2, 3, 5, 6, 10, 15, 30Factors the 75: 1, 3, 5, 15, 25, 75

There room 4 usual factors of 30 and also 75, that space 1, 3, 5, and 15. Therefore, the greatest usual factor the 30 and also 75 is 15.

GCF that 30 and also 75 by Euclidean Algorithm

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

Here X = 75 and also Y = 30

GCF(75, 30) = GCF(30, 75 mod 30) = GCF(30, 15)GCF(30, 15) = GCF(15, 30 mode 15) = GCF(15, 0)GCF(15, 0) = 15 (∵ GCF(X, 0) = |X|, whereby X ≠ 0)

Therefore, the worth of GCF the 30 and 75 is 15.

GCF of 30 and also 75 by prime Factorization

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Prime administer of 30 and 75 is (2 × 3 × 5) and (3 × 5 × 5) respectively. As visible, 30 and also 75 have common prime factors. Hence, the GCF the 30 and also 75 is 3 × 5 = 15.

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GCF that 30 and also 75 Examples


Example 1: For two numbers, GCF = 15 and also LCM = 150. If one number is 30, discover the other number.

Solution:

Given: GCF (x, 30) = 15 and also LCM (x, 30) = 150∵ GCF × LCM = 30 × (x)⇒ x = (GCF × LCM)/30⇒ x = (15 × 150)/30⇒ x = 75Therefore, the various other number is 75.


Example 2: find the GCF the 30 and 75, if your LCM is 150.

Solution:

∵ LCM × GCF = 30 × 75⇒ GCF(30, 75) = (30 × 75)/150 = 15Therefore, the greatest usual factor of 30 and also 75 is 15.


Example 3: uncover the biggest number that divides 30 and 75 exactly.

Solution:

The greatest number that divides 30 and also 75 specifically is your greatest common factor, i.e. GCF of 30 and 75.⇒ determinants of 30 and 75:

Factors the 30 = 1, 2, 3, 5, 6, 10, 15, 30Factors of 75 = 1, 3, 5, 15, 25, 75

Therefore, the GCF that 30 and 75 is 15.


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FAQs top top GCF of 30 and also 75

What is the GCF of 30 and also 75?

The GCF that 30 and also 75 is 15. To calculation the GCF (Greatest usual Factor) that 30 and also 75, we need to element each number (factors the 30 = 1, 2, 3, 5, 6, 10, 15, 30; components of 75 = 1, 3, 5, 15, 25, 75) and choose the greatest aspect that exactly divides both 30 and 75, i.e., 15.

What is the Relation in between LCM and also GCF that 30, 75?

The complying with equation have the right to be offered to refer the relation between LCM and GCF of 30 and 75, i.e. GCF × LCM = 30 × 75.

What room the approaches to discover GCF that 30 and 75?

There are three frequently used approaches to discover the GCF the 30 and also 75.

By Listing usual FactorsBy prime FactorizationBy long Division

How to discover the GCF that 30 and 75 through Long division Method?

To uncover the GCF that 30, 75 utilizing long division method, 75 is divided by 30. The corresponding divisor (15) as soon as remainder equals 0 is taken as GCF.

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How to uncover the GCF of 30 and 75 by prime Factorization?

To discover the GCF the 30 and also 75, us will discover the prime factorization the the provided numbers, i.e. 30 = 2 × 3 × 5; 75 = 3 × 5 × 5.⇒ due to the fact that 3, 5 are common terms in the element factorization of 30 and 75. Hence, GCF(30, 75) = 3 × 5 = 15☛ element Number

If the GCF of 75 and 30 is 15, discover its LCM.

GCF(75, 30) × LCM(75, 30) = 75 × 30Since the GCF the 75 and also 30 = 15⇒ 15 × LCM(75, 30) = 2250Therefore, LCM = 150☛ GCF Calculator