GCF that 25 and also 75 is the largest possible number that divides 25 and also 75 exactly without any remainder. The determinants of 25 and also 75 are 1, 5, 25 and also 1, 3, 5, 15, 25, 75 respectively. There room 3 typically used approaches to find the GCF that 25 and also 75 - element factorization, lengthy division, and also Euclidean algorithm.

You are watching: Greatest common factor of 25 and 75

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

Answer: GCF of 25 and 75 is 25.

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Explanation:

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


Let's look at the different methods for finding the GCF of 25 and also 75.

Prime factorization MethodLong department MethodListing usual Factors

GCF that 25 and also 75 by element Factorization

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Prime administrate of 25 and also 75 is (5 × 5) and also (3 × 5 × 5) respectively. As visible, 25 and also 75 have usual prime factors. Hence, the GCF of 25 and 75 is 5 × 5 = 25.

GCF that 25 and 75 by long Division

GCF that 25 and 75 is the divisor the we obtain when the remainder i do not care 0 ~ doing long division repeatedly.

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

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

GCF of 25 and also 75 by Listing usual Factors

Factors that 25: 1, 5, 25Factors the 75: 1, 3, 5, 15, 25, 75

There space 3 typical factors that 25 and 75, that room 1, 5, and also 25. Therefore, the greatest usual factor that 25 and 75 is 25.

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GCF the 25 and also 75 Examples


Example 1: The product of 2 numbers is 1875. If their GCF is 25, what is their LCM?

Solution:

Given: GCF = 25 and product of numbers = 1875∵ LCM × GCF = product the 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, find 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: find the biggest number that divides 25 and also 75 exactly.

Solution:

The biggest number the divides 25 and also 75 specifically is your greatest typical factor, i.e. GCF that 25 and also 75.⇒ determinants of 25 and 75:

Factors the 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 top top GCF that 25 and 75

What is the GCF that 25 and also 75?

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

What space the approaches to find GCF of 25 and 75?

There are three typically used methods to find the GCF of 25 and also 75.

By Euclidean AlgorithmBy prime FactorizationBy lengthy Division

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

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

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

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

How to find the GCF that 25 and also 75 by Long division Method?

To discover the GCF that 25, 75 utilizing long department method, 75 is divided by 25. The matching divisor (25) when remainder equals 0 is taken together GCF.

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

The following equation can be offered to express the relation between LCM and also GCF the 25 and also 75, i.e. GCF × LCM = 25 × 75.