A day full of math games & activities. Find one near you.

GCF of 10 and 18

GCF of 10 and 18 is the largest possible number that divides 10 and 18 exactly without any remainder. The factors of 10 and 18 are 1, 2, 5, 10 and 1, 2, 3, 6, 9, 18 respectively. There are 3 commonly used methods to find the GCF of 10 and 18 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 10 and 18
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 10 and 18?

Answer: GCF of 10 and 18 is 2.

Explanation:

The GCF of two non-zero integers, x(10) and y(18), is the greatest positive integer m(2) that divides both x(10) and y(18) without any remainder.

Methods to Find GCF of 10 and 18

Let's look at the different methods for finding the GCF of 10 and 18.

Prime Factorization Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 10 and 18 by Prime Factorization

Prime factorization of 10 and 18 is (2 × 5) and (2 × 3 × 3) respectively. As visible, 10 and 18 have only one common prime factor i.e. 2. Hence, the GCF of 10 and 18 is 2.

GCF of 10 and 18 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 = 18 and Y = 10

GCF(18, 10) = GCF(10, 18 mod 10) = GCF(10, 8)
GCF(10, 8) = GCF(8, 10 mod 8) = GCF(8, 2)
GCF(8, 2) = GCF(2, 8 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 10 and 18 is 2.

GCF of 10 and 18 by Listing Common Factors

Factors of 10: 1, 2, 5, 10
Factors of 18: 1, 2, 3, 6, 9, 18

There are 2 common factors of 10 and 18, that are 1 and 2. Therefore, the greatest common factor of 10 and 18 is 2.

☛ Also Check:

GCF of 10 and 18 Examples

Example 1: The product of two numbers is 180. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 180
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 180/2
Therefore, the LCM is 90.
Example 2: Find the greatest number that divides 10 and 18 exactly.

Solution:

The greatest number that divides 10 and 18 exactly is their greatest common factor, i.e. GCF of 10 and 18.
⇒ Factors of 10 and 18:
- Factors of 10 = 1, 2, 5, 10
- Factors of 18 = 1, 2, 3, 6, 9, 18
Therefore, the GCF of 10 and 18 is 2.
Example 3: Find the GCF of 10 and 18, if their LCM is 90.

Solution:

∵ LCM × GCF = 10 × 18
⇒ GCF(10, 18) = (10 × 18)/90 = 2
Therefore, the greatest common factor of 10 and 18 is 2.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on GCF of 10 and 18

What is the GCF of 10 and 18?

The GCF of 10 and 18 is 2. To calculate the GCF (Greatest Common Factor) of 10 and 18, we need to factor each number (factors of 10 = 1, 2, 5, 10; factors of 18 = 1, 2, 3, 6, 9, 18) and choose the greatest factor that exactly divides both 10 and 18, i.e., 2.

How to Find the GCF of 10 and 18 by Long Division Method?

To find the GCF of 10, 18 using long division method, 18 is divided by 10. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 10 and 18?

There are three commonly used methods to find the GCF of 10 and 18.

By Listing Common Factors
By Prime Factorization
By Long Division

What is the Relation Between LCM and GCF of 10, 18?

The following equation can be used to express the relation between LCM and GCF of 10 and 18, i.e. GCF × LCM = 10 × 18.

How to Find the GCF of 10 and 18 by Prime Factorization?

To find the GCF of 10 and 18, we will find the prime factorization of the given numbers, i.e. 10 = 2 × 5; 18 = 2 × 3 × 3.
⇒ Since 2 is the only common prime factor of 10 and 18. Hence, GCF (10, 18) = 2.
☛ What is a Prime Number?

If the GCF of 18 and 10 is 2, Find its LCM.

GCF(18, 10) × LCM(18, 10) = 18 × 10
Since the GCF of 18 and 10 = 2
⇒ 2 × LCM(18, 10) = 180
Therefore, LCM = 90
☛ Greatest Common Factor Calculator

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum