GCF of 25 and also 75 is the largest feasible number the divides 25 and 75 specifically without any remainder. The factors of 25 and also 75 are 1, 5, 25 and 1, 3, 5, 15, 25, 75 respectively. There are 3 frequently used techniques to uncover the GCF that 25 and 75 - prime factorization, lengthy division, and also Euclidean algorithm.

You are watching: What is the gcf of 25 and 75

1.GCF the 25 and 75
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF of 25 and also 75 is 25.

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Explanation:

The GCF of two non-zero integers, x(25) and also y(75), is the greatest positive essence m(25) the divides both x(25) and also y(75) without any remainder.


Let's look at the various methods because that finding the GCF the 25 and also 75.

Prime factorization MethodLong division MethodListing usual Factors

GCF that 25 and 75 by element Factorization

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Prime administer of 25 and 75 is (5 × 5) and also (3 × 5 × 5) respectively. Together visible, 25 and also 75 have typical prime factors. Hence, the GCF of 25 and 75 is 5 × 5 = 25.

GCF the 25 and also 75 by lengthy Division

GCF of 25 and 75 is the divisor the we get when the remainder becomes 0 ~ doing long department repeatedly.

Step 2: because the remainder = 0, the divisor (25) is the GCF the 25 and 75.

The corresponding divisor (25) is the GCF the 25 and also 75.

GCF that 25 and 75 through Listing usual Factors

Factors of 25: 1, 5, 25Factors of 75: 1, 3, 5, 15, 25, 75

There are 3 common factors that 25 and 75, that room 1, 5, and 25. Therefore, the greatest typical factor the 25 and 75 is 25.

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GCF of 25 and also 75 Examples


Example 1: The product of two numbers is 1875. If their GCF is 25, what is your LCM?

Solution:

Given: GCF = 25 and product of number = 1875∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 1875/25Therefore, the LCM is 75.


Example 2: For 2 numbers, GCF = 25 and LCM = 75. If one number is 25, discover the various other number.

Solution:

Given: GCF (y, 25) = 25 and also LCM (y, 25) = 75∵ GCF × LCM = 25 × (y)⇒ y = (GCF × LCM)/25⇒ y = (25 × 75)/25⇒ y = 75Therefore, the other number is 75.


Example 3: uncover the biggest number the divides 25 and 75 exactly.

Solution:

The biggest number that divides 25 and 75 precisely is your greatest common factor, i.e. GCF of 25 and 75.⇒ factors of 25 and 75:

Factors of 25 = 1, 5, 25Factors that 75 = 1, 3, 5, 15, 25, 75

Therefore, the GCF that 25 and also 75 is 25.


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FAQs on GCF of 25 and 75

What is the GCF the 25 and 75?

The GCF that 25 and also 75 is 25. To calculate the GCF (Greatest usual Factor) of 25 and also 75, we need to factor each number (factors the 25 = 1, 5, 25; components of 75 = 1, 3, 5, 15, 25, 75) and also choose the greatest element that specifically divides both 25 and also 75, i.e., 25.

What are the approaches to discover GCF that 25 and also 75?

There space three commonly used approaches to uncover the GCF of 25 and also 75.

By Euclidean AlgorithmBy prime FactorizationBy long Division

If the GCF of 75 and also 25 is 25, uncover its LCM.

GCF(75, 25) × LCM(75, 25) = 75 × 25Since the GCF that 75 and 25 = 25⇒ 25 × LCM(75, 25) = 1875Therefore, LCM = 75☛ GCF Calculator

How to discover the GCF the 25 and 75 by prime Factorization?

To discover the GCF of 25 and also 75, we will find the prime factorization of the provided numbers, i.e. 25 = 5 × 5; 75 = 3 × 5 × 5.⇒ because 5, 5 are typical terms in the prime factorization the 25 and 75. Hence, GCF(25, 75) = 5 × 5 = 25☛ What is a prime Number?

How to find the GCF of 25 and 75 through Long department Method?

To find the GCF the 25, 75 making use of long division method, 75 is split by 25. The equivalent divisor (25) when remainder equates to 0 is taken together GCF.

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What is the Relation in between LCM and GCF the 25, 75?

The complying with equation can be used to express the relation in between LCM and GCF that 25 and 75, i.e. GCF × LCM = 25 × 75.