GCF of 25 and 30 is the largest possible number the divides 25 and also 30 exactly without any type of remainder. The components of 25 and 30 are 1, 5, 25 and 1, 2, 3, 5, 6, 10, 15, 30 respectively. There room 3 generally used approaches to uncover the GCF the 25 and 30 - long division, Euclidean algorithm, and prime factorization.

You are watching: Common factors of 25 and 30

1.GCF of 25 and also 30
2.List the Methods
3.Solved Examples
4.FAQs

Answer: GCF that 25 and 30 is 5.

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Explanation:

The GCF of 2 non-zero integers, x(25) and also y(30), is the greatest positive essence m(5) that divides both x(25) and y(30) without any type of remainder.


Let's look in ~ the different methods for finding the GCF the 25 and 30.

Listing usual FactorsPrime factorization MethodLong department Method

GCF that 25 and also 30 through Listing typical Factors

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

There are 2 usual factors of 25 and 30, that are 1 and 5. Therefore, the greatest common factor of 25 and 30 is 5.

GCF the 25 and 30 by prime Factorization

Prime factorization of 25 and 30 is (5 × 5) and also (2 × 3 × 5) respectively. As visible, 25 and 30 have only one common prime element i.e. 5. Hence, the GCF that 25 and 30 is 5.

GCF of 25 and also 30 by lengthy Division

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GCF the 25 and 30 is the divisor that we acquire when the remainder i do not care 0 after ~ doing long department repeatedly.

Step 2: because the remainder ≠ 0, we will certainly divide the divisor of action 1 (25) through the remainder (5).Step 3: Repeat this process until the remainder = 0.

The matching divisor (5) is the GCF of 25 and also 30.

☛ also Check:


GCF that 25 and also 30 Examples


Example 1: For 2 numbers, GCF = 5 and LCM = 150. If one number is 30, find the various other number.

Solution:

Given: GCF (y, 30) = 5 and also LCM (y, 30) = 150∵ GCF × LCM = 30 × (y)⇒ y = (GCF × LCM)/30⇒ y = (5 × 150)/30⇒ y = 25Therefore, the other number is 25.


Example 2: find the best number that divides 25 and also 30 exactly.

Solution:

The biggest number the divides 25 and also 30 specifically is your greatest common factor, i.e. GCF the 25 and 30.⇒ factors of 25 and also 30:

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

Therefore, the GCF that 25 and 30 is 5.


Example 3: uncover the GCF the 25 and also 30, if your LCM is 150.

Solution:

∵ LCM × GCF = 25 × 30⇒ GCF(25, 30) = (25 × 30)/150 = 5Therefore, the greatest common factor the 25 and 30 is 5.


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FAQs top top GCF that 25 and also 30

What is the GCF that 25 and also 30?

The GCF that 25 and 30 is 5. To calculation the greatest common factor of 25 and also 30, we need to aspect each number (factors of 25 = 1, 5, 25; determinants of 30 = 1, 2, 3, 5, 6, 10, 15, 30) and choose the greatest element that specifically divides both 25 and also 30, i.e., 5.

How to find the GCF that 25 and 30 by element Factorization?

To uncover the GCF of 25 and 30, us will uncover the element factorization that the provided numbers, i.e. 25 = 5 × 5; 30 = 2 × 3 × 5.⇒ due to the fact that 5 is the only typical prime factor of 25 and also 30. Hence, GCF (25, 30) = 5.☛ What space Prime Numbers?

What space the approaches to discover GCF of 25 and also 30?

There are three typically used techniques to uncover the GCF of 25 and 30.

By long DivisionBy Euclidean AlgorithmBy prime Factorization

What is the Relation in between LCM and also GCF the 25, 30?

The adhering to equation deserve to be offered to refer the relation between Least common Multiple and GCF that 25 and also 30, i.e. GCF × LCM = 25 × 30.

How to find the GCF that 25 and 30 by Long department Method?

To uncover the GCF of 25, 30 utilizing long division method, 30 is divided by 25. The equivalent divisor (5) once remainder amounts to 0 is taken as GCF.

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If the GCF of 30 and 25 is 5, find its LCM.

GCF(30, 25) × LCM(30, 25) = 30 × 25Since the GCF of 30 and 25 = 5⇒ 5 × LCM(30, 25) = 750Therefore, LCM = 150☛ GCF Calculator