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GCF of 45 and 80

GCF of 45 and 80 is the largest possible number that divides 45 and 80 exactly without any remainder. The factors of 45 and 80 are 1, 3, 5, 9, 15, 45 and 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 respectively. There are 3 commonly used methods to find the GCF of 45 and 80 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 45 and 80
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 45 and 80?

Answer: GCF of 45 and 80 is 5.

Explanation:

The GCF of two non-zero integers, x(45) and y(80), is the greatest positive integer m(5) that divides both x(45) and y(80) without any remainder.

Methods to Find GCF of 45 and 80

Let's look at the different methods for finding the GCF of 45 and 80.

Prime Factorization Method
Using Euclid's Algorithm
Long Division Method

GCF of 45 and 80 by Prime Factorization

Prime factorization of 45 and 80 is (3 × 3 × 5) and (2 × 2 × 2 × 2 × 5) respectively. As visible, 45 and 80 have only one common prime factor i.e. 5. Hence, the GCF of 45 and 80 is 5.

GCF of 45 and 80 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 = 80 and Y = 45

GCF(80, 45) = GCF(45, 80 mod 45) = GCF(45, 35)
GCF(45, 35) = GCF(35, 45 mod 35) = GCF(35, 10)
GCF(35, 10) = GCF(10, 35 mod 10) = GCF(10, 5)
GCF(10, 5) = GCF(5, 10 mod 5) = GCF(5, 0)
GCF(5, 0) = 5 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 45 and 80 is 5.

GCF of 45 and 80 by Long Division

GCF of 45 and 80 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 80 (larger number) by 45 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (45) by the remainder (35).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 45 and 80.

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GCF of 45 and 80 Examples

Example 1: For two numbers, GCF = 5 and LCM = 720. If one number is 80, find the other number.

Solution:

Given: GCF (x, 80) = 5 and LCM (x, 80) = 720
∵ GCF × LCM = 80 × (x)
⇒ x = (GCF × LCM)/80
⇒ x = (5 × 720)/80
⇒ x = 45
Therefore, the other number is 45.
Example 2: The product of two numbers is 3600. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 3600
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 3600/5
Therefore, the LCM is 720.
Example 3: Find the greatest number that divides 45 and 80 exactly.

Solution:

The greatest number that divides 45 and 80 exactly is their greatest common factor, i.e. GCF of 45 and 80.
⇒ Factors of 45 and 80:
- Factors of 45 = 1, 3, 5, 9, 15, 45
- Factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Therefore, the GCF of 45 and 80 is 5.

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FAQs on GCF of 45 and 80

What is the GCF of 45 and 80?

The GCF of 45 and 80 is 5. To calculate the greatest common factor of 45 and 80, we need to factor each number (factors of 45 = 1, 3, 5, 9, 15, 45; factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80) and choose the greatest factor that exactly divides both 45 and 80, i.e., 5.

What are the Methods to Find GCF of 45 and 80?

There are three commonly used methods to find the GCF of 45 and 80.

By Prime Factorization
By Euclidean Algorithm
By Long Division

If the GCF of 80 and 45 is 5, Find its LCM.

GCF(80, 45) × LCM(80, 45) = 80 × 45
Since the GCF of 80 and 45 = 5
⇒ 5 × LCM(80, 45) = 3600
Therefore, LCM = 720
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How to Find the GCF of 45 and 80 by Long Division Method?

To find the GCF of 45, 80 using long division method, 80 is divided by 45. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 45, 80?

The following equation can be used to express the relation between Least Common Multiple and GCF of 45 and 80, i.e. GCF × LCM = 45 × 80.

How to Find the GCF of 45 and 80 by Prime Factorization?

To find the GCF of 45 and 80, we will find the prime factorization of the given numbers, i.e. 45 = 3 × 3 × 5; 80 = 2 × 2 × 2 × 2 × 5.
⇒ Since 5 is the only common prime factor of 45 and 80. Hence, GCF (45, 80) = 5.
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