GCF the 30 and also 75 is the largest feasible number the divides 30 and 75 specifically without any kind of remainder. The factors of 30 and 75 room 1, 2, 3, 5, 6, 10, 15, 30 and 1, 3, 5, 15, 25, 75 respectively. There are 3 typically used approaches to find the GCF that 30 and 75 - lengthy division, Euclidean algorithm, and also prime factorization.

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

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

Answer: GCF of 30 and 75 is 15.

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Explanation:

The GCF of 2 non-zero integers, x(30) and y(75), is the biggest positive integer m(15) that divides both x(30) and also y(75) without any type of remainder.


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

Listing typical FactorsUsing Euclid's AlgorithmPrime administer Method

GCF that 30 and also 75 by 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 are 4 typical factors of 30 and 75, that space 1, 3, 5, and 15. Therefore, the greatest typical factor that 30 and 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 Y = 30

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

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

GCF that 30 and also 75 by element Factorization

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

☛ additionally Check:


GCF the 30 and 75 Examples


Example 1: For two numbers, GCF = 15 and 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: discover the GCF the 30 and 75, if their LCM is 150.

Solution:

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


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

Solution:

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

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

Therefore, the GCF the 30 and also 75 is 15.


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FAQs top top GCF the 30 and 75

What is the GCF the 30 and also 75?

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

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

The complying with equation deserve to be supplied to to express the relation between LCM and GCF that 30 and 75, i.e. GCF × LCM = 30 × 75.

What space the techniques to discover GCF that 30 and also 75?

There space three generally used techniques to discover the GCF that 30 and 75.

By Listing common FactorsBy prime FactorizationBy lengthy Division

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

To find the GCF of 30, 75 utilizing long division method, 75 is divided by 30. The matching divisor (15) when remainder equals 0 is taken together GCF.

See more: How Many Birthdays Does An Average Man Have ? How Many Birthdays Does The Average Man Have

How to discover the GCF of 30 and 75 by element Factorization?

To uncover the GCF that 30 and also 75, us will find the element factorization of 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 prime factorization of 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 the 75 and 30 = 15⇒ 15 × LCM(75, 30) = 2250Therefore, LCM = 150☛ GCF Calculator