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GCF of 25 and 49

GCF of 25 and 49 is the largest possible number that divides 25 and 49 exactly without any remainder. The factors of 25 and 49 are 1, 5, 25 and 1, 7, 49 respectively. There are 3 commonly used methods to find the GCF of 25 and 49 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 25 and 49
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 25 and 49?

Answer: GCF of 25 and 49 is 1.

Explanation:

The GCF of two non-zero integers, x(25) and y(49), is the greatest positive integer m(1) that divides both x(25) and y(49) without any remainder.

Methods to Find GCF of 25 and 49

The methods to find the GCF of 25 and 49 are explained below.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 25 and 49 by Listing Common Factors

Factors of 25: 1, 5, 25
Factors of 49: 1, 7, 49

Since, 1 is the only common factor between 25 and 49. The Greatest Common Factor of 25 and 49 is 1.

GCF of 25 and 49 by Long Division

GCF of 25 and 49 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 49 (larger number) by 25 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (25) by the remainder (24).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 25 and 49.

GCF of 25 and 49 by Prime Factorization

Prime factorization of 25 and 49 is (5 × 5) and (7 × 7) respectively. As visible, there are no common prime factors between 25 and 49, i.e. they are co-prime. Hence, the GCF of 25 and 49 will be 1.

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GCF of 25 and 49 Examples

Example 1: Find the GCF of 25 and 49, if their LCM is 1225.

Solution:

∵ LCM × GCF = 25 × 49
⇒ GCF(25, 49) = (25 × 49)/1225 = 1
Therefore, the greatest common factor of 25 and 49 is 1.
Example 2: Find the greatest number that divides 25 and 49 exactly.

Solution:

The greatest number that divides 25 and 49 exactly is their greatest common factor, i.e. GCF of 25 and 49.
⇒ Factors of 25 and 49:
- Factors of 25 = 1, 5, 25
- Factors of 49 = 1, 7, 49
Therefore, the GCF of 25 and 49 is 1.
Example 3: For two numbers, GCF = 1 and LCM = 1225. If one number is 25, find the other number.

Solution:

Given: GCF (x, 25) = 1 and LCM (x, 25) = 1225
∵ GCF × LCM = 25 × (x)
⇒ x = (GCF × LCM)/25
⇒ x = (1 × 1225)/25
⇒ x = 49
Therefore, the other number is 49.

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FAQs on GCF of 25 and 49

What is the GCF of 25 and 49?

The GCF of 25 and 49 is 1. To calculate the GCF (Greatest Common Factor) of 25 and 49, we need to factor each number (factors of 25 = 1, 5, 25; factors of 49 = 1, 7, 49) and choose the greatest factor that exactly divides both 25 and 49, i.e., 1.

How to Find the GCF of 25 and 49 by Long Division Method?

To find the GCF of 25, 49 using long division method, 49 is divided by 25. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

How to Find the GCF of 25 and 49 by Prime Factorization?

To find the GCF of 25 and 49, we will find the prime factorization of the given numbers, i.e. 25 = 5 × 5; 49 = 7 × 7.
⇒ There is no common prime factor for 25 and 49. Hence, GCF (25, 49) = 1.
☛ Prime Numbers

What are the Methods to Find GCF of 25 and 49?

There are three commonly used methods to find the GCF of 25 and 49.

By Euclidean Algorithm
By Long Division
By Prime Factorization

If the GCF of 49 and 25 is 1, Find its LCM.

GCF(49, 25) × LCM(49, 25) = 49 × 25
Since the GCF of 49 and 25 = 1
⇒ 1 × LCM(49, 25) = 1225
Therefore, LCM = 1225
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 25, 49?

The following equation can be used to express the relation between LCM and GCF of 25 and 49, i.e. GCF × LCM = 25 × 49.

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