GCF that 25 and 40 is the largest feasible number that divides 25 and 40 specifically without any remainder. The components of 25 and also 40 space 1, 5, 25 and 1, 2, 4, 5, 8, 10, 20, 40 respectively. There room 3 typically used methods to uncover the GCF of 25 and also 40 - Euclidean algorithm, prime factorization, and long division.

You are watching: What is the greatest common factor of 25 and 40

1.GCF the 25 and 40
2.List the Methods
3.Solved Examples
4.FAQs

Answer: GCF the 25 and also 40 is 5.

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Explanation:

The GCF of two non-zero integers, x(25) and also y(40), is the greatest positive essence m(5) that divides both x(25) and y(40) without any type of remainder.


Let's look in ~ the various methods because that finding the GCF the 25 and 40.

Long division MethodListing usual FactorsPrime administer Method

GCF of 25 and also 40 by lengthy Division

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GCF of 25 and also 40 is the divisor the we acquire when the remainder i do not care 0 ~ doing long division repeatedly.

Step 2: because the remainder ≠ 0, we will certainly divide the divisor of action 1 (25) through the remainder (15).Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF that 25 and also 40.

GCF of 25 and also 40 through Listing common Factors

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Factors of 25: 1, 5, 25Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

There room 2 common factors that 25 and 40, that are 1 and 5. Therefore, the greatest typical factor that 25 and 40 is 5.

GCF the 25 and also 40 by element Factorization

Prime factorization of 25 and 40 is (5 × 5) and also (2 × 2 × 2 × 5) respectively. As visible, 25 and 40 have actually only one common prime aspect i.e. 5. Hence, the GCF the 25 and 40 is 5.

☛ likewise Check:


GCF of 25 and 40 Examples


Example 1: find the greatest number the divides 25 and also 40 exactly.

Solution:

The best number the divides 25 and also 40 exactly is their greatest usual factor, i.e. GCF that 25 and also 40.⇒ components of 25 and 40:

Factors that 25 = 1, 5, 25Factors that 40 = 1, 2, 4, 5, 8, 10, 20, 40

Therefore, the GCF that 25 and also 40 is 5.


Example 2: find the GCF of 25 and also 40, if your LCM is 200.

Solution:

∵ LCM × GCF = 25 × 40⇒ GCF(25, 40) = (25 × 40)/200 = 5Therefore, the greatest typical factor of 25 and also 40 is 5.


Example 3: The product of two numbers is 1000. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and also product of numbers = 1000∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 1000/5Therefore, the LCM is 200.


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FAQs top top GCF that 25 and also 40

What is the GCF the 25 and also 40?

The GCF the 25 and 40 is 5. To calculation the GCF the 25 and also 40, we need to factor each number (factors the 25 = 1, 5, 25; components of 40 = 1, 2, 4, 5, 8, 10, 20, 40) and also choose the greatest element that precisely divides both 25 and also 40, i.e., 5.

What are the techniques to uncover GCF the 25 and also 40?

There space three generally used methods to uncover the GCF that 25 and 40.

By prime FactorizationBy lengthy DivisionBy Listing typical Factors

If the GCF the 40 and also 25 is 5, find its LCM.

GCF(40, 25) × LCM(40, 25) = 40 × 25Since the GCF the 40 and 25 = 5⇒ 5 × LCM(40, 25) = 1000Therefore, LCM = 200☛ GCF Calculator

What is the Relation between LCM and GCF that 25, 40?

The adhering to equation deserve to be supplied to to express the relation between LCM and GCF that 25 and 40, i.e. GCF × LCM = 25 × 40.

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How to uncover the GCF the 25 and 40 by Long division Method?

To uncover the GCF of 25, 40 utilizing long department method, 40 is split by 25. The equivalent divisor (5) once remainder amounts to 0 is taken together GCF.

How to find the GCF of 25 and also 40 by prime Factorization?

To uncover the GCF that 25 and also 40, we will discover the prime factorization the the given numbers, i.e. 25 = 5 × 5; 40 = 2 × 2 × 2 × 5.⇒ since 5 is the only typical prime factor of 25 and also 40. Hence, GCF (25, 40) = 5.☛ prime Number