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GCF of 175 and 25

GCF of 175 and 25 is the largest possible number that divides 175 and 25 exactly without any remainder. The factors of 175 and 25 are 1, 5, 7, 25, 35, 175 and 1, 5, 25 respectively. There are 3 commonly used methods to find the GCF of 175 and 25 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 175 and 25
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 175 and 25?

Answer: GCF of 175 and 25 is 25.

Explanation:

The GCF of two non-zero integers, x(175) and y(25), is the greatest positive integer m(25) that divides both x(175) and y(25) without any remainder.

Methods to Find GCF of 175 and 25

The methods to find the GCF of 175 and 25 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 175 and 25 by Listing Common Factors

Factors of 175: 1, 5, 7, 25, 35, 175
Factors of 25: 1, 5, 25

There are 3 common factors of 175 and 25, that are 1, 5, and 25. Therefore, the greatest common factor of 175 and 25 is 25.

GCF of 175 and 25 by Prime Factorization

Prime factorization of 175 and 25 is (5 × 5 × 7) and (5 × 5) respectively. As visible, 175 and 25 have common prime factors. Hence, the GCF of 175 and 25 is 5 × 5 = 25.

GCF of 175 and 25 by Long Division

GCF of 175 and 25 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 175 (larger number) by 25 (smaller number).
Step 2: Since the remainder = 0, the divisor (25) is the GCF of 175 and 25.

The corresponding divisor (25) is the GCF of 175 and 25.

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GCF of 175 and 25 Examples

Example 1: Find the GCF of 175 and 25, if their LCM is 175.

Solution:

∵ LCM × GCF = 175 × 25
⇒ GCF(175, 25) = (175 × 25)/175 = 25
Therefore, the greatest common factor of 175 and 25 is 25.
Example 2: The product of two numbers is 4375. If their GCF is 25, what is their LCM?

Solution:

Given: GCF = 25 and product of numbers = 4375
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 4375/25
Therefore, the LCM is 175.
Example 3: For two numbers, GCF = 25 and LCM = 175. If one number is 175, find the other number.

Solution:

Given: GCF (z, 175) = 25 and LCM (z, 175) = 175
∵ GCF × LCM = 175 × (z)
⇒ z = (GCF × LCM)/175
⇒ z = (25 × 175)/175
⇒ z = 25
Therefore, the other number is 25.

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FAQs on GCF of 175 and 25

What is the GCF of 175 and 25?

The GCF of 175 and 25 is 25. To calculate the GCF of 175 and 25, we need to factor each number (factors of 175 = 1, 5, 7, 25, 35, 175; factors of 25 = 1, 5, 25) and choose the greatest factor that exactly divides both 175 and 25, i.e., 25.

How to Find the GCF of 175 and 25 by Long Division Method?

To find the GCF of 175, 25 using long division method, 175 is divided by 25. The corresponding divisor (25) when remainder equals 0 is taken as GCF.

If the GCF of 25 and 175 is 25, Find its LCM.

GCF(25, 175) × LCM(25, 175) = 25 × 175
Since the GCF of 25 and 175 = 25
⇒ 25 × LCM(25, 175) = 4375
Therefore, LCM = 175
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What are the Methods to Find GCF of 175 and 25?

There are three commonly used methods to find the GCF of 175 and 25.

By Prime Factorization
By Euclidean Algorithm
By Long Division

What is the Relation Between LCM and GCF of 175, 25?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 175 and 25, i.e. GCF × LCM = 175 × 25.

How to Find the GCF of 175 and 25 by Prime Factorization?

To find the GCF of 175 and 25, we will find the prime factorization of the given numbers, i.e. 175 = 5 × 5 × 7; 25 = 5 × 5.
⇒ Since 5, 5 are common terms in the prime factorization of 175 and 25. Hence, GCF(175, 25) = 5 × 5 = 25
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