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GCF of 5 and 45

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

1.	GCF of 5 and 45
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 5 and 45?

Answer: GCF of 5 and 45 is 5.

Explanation:

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

Methods to Find GCF of 5 and 45

Let's look at the different methods for finding the GCF of 5 and 45.

Listing Common Factors
Long Division Method
Using Euclid's Algorithm

GCF of 5 and 45 by Listing Common Factors

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

There are 2 common factors of 5 and 45, that are 1 and 5. Therefore, the greatest common factor of 5 and 45 is 5.

GCF of 5 and 45 by Long Division

GCF of 5 and 45 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 45 (larger number) by 5 (smaller number).
Step 2: Since the remainder = 0, the divisor (5) is the GCF of 5 and 45.

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

GCF of 5 and 45 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 = 45 and Y = 5

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

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

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GCF of 5 and 45 Examples

Example 1: Find the GCF of 5 and 45, if their LCM is 45.

Solution:

∵ LCM × GCF = 5 × 45
⇒ GCF(5, 45) = (5 × 45)/45 = 5
Therefore, the greatest common factor of 5 and 45 is 5.
Example 2: Find the greatest number that divides 5 and 45 exactly.

Solution:

The greatest number that divides 5 and 45 exactly is their greatest common factor, i.e. GCF of 5 and 45.
⇒ Factors of 5 and 45:
- Factors of 5 = 1, 5
- Factors of 45 = 1, 3, 5, 9, 15, 45
Therefore, the GCF of 5 and 45 is 5.
Example 3: The product of two numbers is 225. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 225
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 225/5
Therefore, the LCM is 45.

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FAQs on GCF of 5 and 45

What is the GCF of 5 and 45?

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

What are the Methods to Find GCF of 5 and 45?

There are three commonly used methods to find the GCF of 5 and 45.

By Prime Factorization
By Euclidean Algorithm
By Long Division

What is the Relation Between LCM and GCF of 5, 45?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 5 and 45, i.e. GCF × LCM = 5 × 45.

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

GCF(45, 5) × LCM(45, 5) = 45 × 5
Since the GCF of 45 and 5 = 5
⇒ 5 × LCM(45, 5) = 225
Therefore, LCM = 45
☛ Greatest Common Factor Calculator

How to Find the GCF of 5 and 45 by Long Division Method?

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

How to Find the GCF of 5 and 45 by Prime Factorization?

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