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GCF of 12 and 25

GCF of 12 and 25 is the largest possible number that divides 12 and 25 exactly without any remainder. The factors of 12 and 25 are 1, 2, 3, 4, 6, 12 and 1, 5, 25 respectively. There are 3 commonly used methods to find the GCF of 12 and 25 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 12 and 25
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 12 and 25?

Answer: GCF of 12 and 25 is 1.

Explanation:

The GCF of two non-zero integers, x(12) and y(25), is the greatest positive integer m(1) that divides both x(12) and y(25) without any remainder.

Methods to Find GCF of 12 and 25

Let's look at the different methods for finding the GCF of 12 and 25.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

GCF of 12 and 25 by Long Division

GCF of 12 and 25 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 25 (larger number) by 12 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (1).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 12 and 25.

GCF of 12 and 25 by Prime Factorization

Prime factorization of 12 and 25 is (2 × 2 × 3) and (5 × 5) respectively. As visible, there are no common prime factors between 12 and 25, i.e. they are coprime. Hence, the GCF of 12 and 25 will be 1.

GCF of 12 and 25 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 25 and Y = 12

GCF(25, 12) = GCF(12, 25 mod 12) = GCF(12, 1)
GCF(12, 1) = GCF(1, 12 mod 1) = GCF(1, 0)
GCF(1, 0) = 1 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 12 and 25 is 1.

☛ Also Check:

GCF of 12 and 25 Examples

Example 1: For two numbers, GCF = 1 and LCM = 300. If one number is 25, find the other number.

Solution:

Given: GCF (x, 25) = 1 and LCM (x, 25) = 300
∵ GCF × LCM = 25 × (x)
⇒ x = (GCF × LCM)/25
⇒ x = (1 × 300)/25
⇒ x = 12
Therefore, the other number is 12.
Example 2: The product of two numbers is 300. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 300
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 300/1
Therefore, the LCM is 300.
Example 3: Find the GCF of 12 and 25, if their LCM is 300.

Solution:

∵ LCM × GCF = 12 × 25
⇒ GCF(12, 25) = (12 × 25)/300 = 1
Therefore, the greatest common factor of 12 and 25 is 1.

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FAQs on GCF of 12 and 25

What is the GCF of 12 and 25?

The GCF of 12 and 25 is 1. To calculate the GCF (Greatest Common Factor) of 12 and 25, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 25 = 1, 5, 25) and choose the greatest factor that exactly divides both 12 and 25, i.e., 1.

How to Find the GCF of 12 and 25 by Prime Factorization?

To find the GCF of 12 and 25, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 25 = 5 × 5.
⇒ There is no common prime factor for 12 and 25. Hence, GCF (12, 25) = 1.
☛ What are Prime Numbers?

How to Find the GCF of 12 and 25 by Long Division Method?

To find the GCF of 12, 25 using long division method, 25 is divided by 12. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 12 and 25?

There are three commonly used methods to find the GCF of 12 and 25.

By Prime Factorization
By Long Division
By Listing Common Factors

If the GCF of 25 and 12 is 1, Find its LCM.

GCF(25, 12) × LCM(25, 12) = 25 × 12
Since the GCF of 25 and 12 = 1
⇒ 1 × LCM(25, 12) = 300
Therefore, LCM = 300
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 12, 25?

The following equation can be used to express the relation between Least Common Multiple and GCF of 12 and 25, i.e. GCF × LCM = 12 × 25.

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