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

GCF of 45 and 81

GCF of 45 and 81 is the largest possible number that divides 45 and 81 exactly without any remainder. The factors of 45 and 81 are 1, 3, 5, 9, 15, 45 and 1, 3, 9, 27, 81 respectively. There are 3 commonly used methods to find the GCF of 45 and 81 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 45 and 81
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 45 and 81?

Answer: GCF of 45 and 81 is 9.

Explanation:

The GCF of two non-zero integers, x(45) and y(81), is the greatest positive integer m(9) that divides both x(45) and y(81) without any remainder.

Methods to Find GCF of 45 and 81

The methods to find the GCF of 45 and 81 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 45 and 81 by Prime Factorization

Prime factorization of 45 and 81 is (3 × 3 × 5) and (3 × 3 × 3 × 3) respectively. As visible, 45 and 81 have common prime factors. Hence, the GCF of 45 and 81 is 3 × 3 = 9.

GCF of 45 and 81 by Listing Common Factors

Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 81: 1, 3, 9, 27, 81

There are 3 common factors of 45 and 81, that are 1, 3, and 9. Therefore, the greatest common factor of 45 and 81 is 9.

GCF of 45 and 81 by Long Division

GCF of 45 and 81 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 81 (larger number) by 45 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (45) by the remainder (36).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (9) is the GCF of 45 and 81.

☛ Also Check:

GCF of 45 and 81 Examples

Example 1: Find the greatest number that divides 45 and 81 exactly.

Solution:

The greatest number that divides 45 and 81 exactly is their greatest common factor, i.e. GCF of 45 and 81.
⇒ Factors of 45 and 81:
- Factors of 45 = 1, 3, 5, 9, 15, 45
- Factors of 81 = 1, 3, 9, 27, 81
Therefore, the GCF of 45 and 81 is 9.
Example 2: Find the GCF of 45 and 81, if their LCM is 405.

Solution:

∵ LCM × GCF = 45 × 81
⇒ GCF(45, 81) = (45 × 81)/405 = 9
Therefore, the greatest common factor of 45 and 81 is 9.
Example 3: The product of two numbers is 3645. If their GCF is 9, what is their LCM?

Solution:

Given: GCF = 9 and product of numbers = 3645
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 3645/9
Therefore, the LCM is 405.

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 45 and 81

What is the GCF of 45 and 81?

The GCF of 45 and 81 is 9. To calculate the GCF of 45 and 81, we need to factor each number (factors of 45 = 1, 3, 5, 9, 15, 45; factors of 81 = 1, 3, 9, 27, 81) and choose the greatest factor that exactly divides both 45 and 81, i.e., 9.

What are the Methods to Find GCF of 45 and 81?

There are three commonly used methods to find the GCF of 45 and 81.

By Euclidean Algorithm
By Prime Factorization
By Long Division

If the GCF of 81 and 45 is 9, Find its LCM.

GCF(81, 45) × LCM(81, 45) = 81 × 45
Since the GCF of 81 and 45 = 9
⇒ 9 × LCM(81, 45) = 3645
Therefore, LCM = 405
☛ Greatest Common Factor Calculator

How to Find the GCF of 45 and 81 by Long Division Method?

To find the GCF of 45, 81 using long division method, 81 is divided by 45. The corresponding divisor (9) when remainder equals 0 is taken as GCF.

How to Find the GCF of 45 and 81 by Prime Factorization?

To find the GCF of 45 and 81, we will find the prime factorization of the given numbers, i.e. 45 = 3 × 3 × 5; 81 = 3 × 3 × 3 × 3.
⇒ Since 3, 3 are common terms in the prime factorization of 45 and 81. Hence, GCF(45, 81) = 3 × 3 = 9
☛ What is a Prime Number?

What is the Relation Between LCM and GCF of 45, 81?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 45 and 81, i.e. GCF × LCM = 45 × 81.

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum