GCF of 30 and 75 is the largest feasible number that divides 30 and also 75 precisely without any kind of remainder. The components of 30 and 75 are 1, 2, 3, 5, 6, 10, 15, 30 and 1, 3, 5, 15, 25, 75 respectively. There space 3 frequently used approaches to discover the GCF that 30 and also 75 - long division, Euclidean algorithm, and prime factorization.

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

Answer: GCF of 30 and 75 is 15.

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Explanation:

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


The techniques to find the GCF the 30 and also 75 are described below.

Listing common FactorsUsing Euclid's AlgorithmPrime administer Method

GCF of 30 and 75 by Listing usual Factors

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

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

GCF of 30 and 75 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 = 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|, where X ≠ 0)

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

GCF of 30 and also 75 by prime Factorization

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

☛ likewise Check:


GCF that 30 and also 75 Examples


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

Solution:

Given: GCF (x, 30) = 15 and 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: discover the GCF of 30 and 75, if their LCM is 150.

Solution:

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


Example 3: find the greatest number the divides 30 and also 75 exactly.

Solution:

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

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

Therefore, the GCF of 30 and 75 is 15.


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FAQs ~ above GCF the 30 and also 75

What is the GCF the 30 and also 75?

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

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

The adhering to equation have the right to be offered to express the relation in between LCM and also GCF that 30 and 75, i.e. GCF × LCM = 30 × 75.

What room the methods to discover GCF that 30 and also 75?

There are three typically used methods to discover the GCF of 30 and also 75.

By Listing usual FactorsBy prime FactorizationBy lengthy Division

How to discover the GCF of 30 and 75 through Long department Method?

To find the GCF of 30, 75 using long department method, 75 is split by 30. The equivalent divisor (15) once remainder equals 0 is taken as GCF.

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How to find the GCF the 30 and also 75 by prime Factorization?

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

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

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