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GCF of 25 and 35

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

1.	GCF of 25 and 35
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 25 and 35?

Answer: GCF of 25 and 35 is 5.

Explanation:

The GCF of two non-zero integers, x(25) and y(35), is the greatest positive integer m(5) that divides both x(25) and y(35) without any remainder.

Methods to Find GCF of 25 and 35

The methods to find the GCF of 25 and 35 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 25 and 35 by Listing Common Factors

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

There are 2 common factors of 25 and 35, that are 1 and 5. Therefore, the greatest common factor of 25 and 35 is 5.

GCF of 25 and 35 by Prime Factorization

Prime factorization of 25 and 35 is (5 × 5) and (5 × 7) respectively. As visible, 25 and 35 have only one common prime factor i.e. 5. Hence, the GCF of 25 and 35 is 5.

GCF of 25 and 35 by Long Division

GCF of 25 and 35 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 35 (larger number) by 25 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (25) by the remainder (10).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 25 and 35.

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GCF of 25 and 35 Examples

Example 1: Find the greatest number that divides 25 and 35 exactly.

Solution:

The greatest number that divides 25 and 35 exactly is their greatest common factor, i.e. GCF of 25 and 35.
⇒ Factors of 25 and 35:
- Factors of 25 = 1, 5, 25
- Factors of 35 = 1, 5, 7, 35
Therefore, the GCF of 25 and 35 is 5.
Example 2: Find the GCF of 25 and 35, if their LCM is 175.

Solution:

∵ LCM × GCF = 25 × 35
⇒ GCF(25, 35) = (25 × 35)/175 = 5
Therefore, the greatest common factor of 25 and 35 is 5.
Example 3: For two numbers, GCF = 5 and LCM = 175. If one number is 35, find the other number.

Solution:

Given: GCF (z, 35) = 5 and LCM (z, 35) = 175
∵ GCF × LCM = 35 × (z)
⇒ z = (GCF × LCM)/35
⇒ z = (5 × 175)/35
⇒ z = 25
Therefore, the other number is 25.

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FAQs on GCF of 25 and 35

What is the GCF of 25 and 35?

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

If the GCF of 35 and 25 is 5, Find its LCM.

GCF(35, 25) × LCM(35, 25) = 35 × 25
Since the GCF of 35 and 25 = 5
⇒ 5 × LCM(35, 25) = 875
Therefore, LCM = 175
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 25, 35?

The following equation can be used to express the relation between LCM and GCF of 25 and 35, i.e. GCF × LCM = 25 × 35.

How to Find the GCF of 25 and 35 by Long Division Method?

To find the GCF of 25, 35 using long division method, 35 is divided by 25. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 25 and 35?

There are three commonly used methods to find the GCF of 25 and 35.

By Listing Common Factors
By Long Division
By Prime Factorization

How to Find the GCF of 25 and 35 by Prime Factorization?

To find the GCF of 25 and 35, we will find the prime factorization of the given numbers, i.e. 25 = 5 × 5; 35 = 5 × 7.
⇒ Since 5 is the only common prime factor of 25 and 35. Hence, GCF (25, 35) = 5.
☛ What are Prime Numbers?

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