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GCF of 18 and 25

GCF of 18 and 25 is the largest possible number that divides 18 and 25 exactly without any remainder. The factors of 18 and 25 are 1, 2, 3, 6, 9, 18 and 1, 5, 25 respectively. There are 3 commonly used methods to find the GCF of 18 and 25 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 18 and 25
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 18 and 25?

Answer: GCF of 18 and 25 is 1.

Explanation:

The GCF of two non-zero integers, x(18) and y(25), is the greatest positive integer m(1) that divides both x(18) and y(25) without any remainder.

Methods to Find GCF of 18 and 25

Let's look at the different methods for finding the GCF of 18 and 25.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 18 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 = 18

GCF(25, 18) = GCF(18, 25 mod 18) = GCF(18, 7)
GCF(18, 7) = GCF(7, 18 mod 7) = GCF(7, 4)
GCF(7, 4) = GCF(4, 7 mod 4) = GCF(4, 3)
GCF(4, 3) = GCF(3, 4 mod 3) = GCF(3, 1)
GCF(3, 1) = 1 (∵ GCF(X, 1) = 1)

Therefore, the value of GCF of 18 and 25 is 1.

GCF of 18 and 25 by Long Division

GCF of 18 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 18 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (7).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 18 and 25.

GCF of 18 and 25 by Listing Common Factors

Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 25: 1, 5, 25

Since, 1 is the only common factor between 18 and 25. The Greatest Common Factor of 18 and 25 is 1.

☛ Also Check:

GCF of 18 and 25 Examples

Example 1: Find the greatest number that divides 18 and 25 exactly.

Solution:

The greatest number that divides 18 and 25 exactly is their greatest common factor, i.e. GCF of 18 and 25.
⇒ Factors of 18 and 25:
- Factors of 18 = 1, 2, 3, 6, 9, 18
- Factors of 25 = 1, 5, 25
Therefore, the GCF of 18 and 25 is 1.
Example 2: The product of two numbers is 450. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 450
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 450/1
Therefore, the LCM is 450.
Example 3: Find the GCF of 18 and 25, if their LCM is 450.

Solution:

∵ LCM × GCF = 18 × 25
⇒ GCF(18, 25) = (18 × 25)/450 = 1
Therefore, the greatest common factor of 18 and 25 is 1.

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FAQs on GCF of 18 and 25

What is the GCF of 18 and 25?

The GCF of 18 and 25 is 1. To calculate the GCF (Greatest Common Factor) of 18 and 25, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 25 = 1, 5, 25) and choose the greatest factor that exactly divides both 18 and 25, i.e., 1.

How to Find the GCF of 18 and 25 by Prime Factorization?

To find the GCF of 18 and 25, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 25 = 5 × 5.
⇒ There is no common prime factor for 18 and 25. Hence, GCF (18, 25) = 1.
☛ What are Prime Numbers?

What are the Methods to Find GCF of 18 and 25?

There are three commonly used methods to find the GCF of 18 and 25.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 18 and 25 by Long Division Method?

To find the GCF of 18, 25 using long division method, 25 is divided by 18. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

If the GCF of 25 and 18 is 1, Find its LCM.

GCF(25, 18) × LCM(25, 18) = 25 × 18
Since the GCF of 25 and 18 = 1
⇒ 1 × LCM(25, 18) = 450
Therefore, LCM = 450
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 18, 25?

The following equation can be used to express the relation between Least Common Multiple and GCF of 18 and 25, i.e. GCF × LCM = 18 × 25.

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