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GCF of 20 and 45

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

1.	GCF of 20 and 45
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 20 and 45?

Answer: GCF of 20 and 45 is 5.

Explanation:

The GCF of two non-zero integers, x(20) and y(45), is the greatest positive integer m(5) that divides both x(20) and y(45) without any remainder.

Methods to Find GCF of 20 and 45

The methods to find the GCF of 20 and 45 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 20 and 45 by Long Division

GCF of 20 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 20 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (20) by the remainder (5).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 20 and 45.

GCF of 20 and 45 by Prime Factorization

Prime factorization of 20 and 45 is (2 × 2 × 5) and (3 × 3 × 5) respectively. As visible, 20 and 45 have only one common prime factor i.e. 5. Hence, the GCF of 20 and 45 is 5.

GCF of 20 and 45 by Listing Common Factors

Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 45: 1, 3, 5, 9, 15, 45

There are 2 common factors of 20 and 45, that are 1 and 5. Therefore, the greatest common factor of 20 and 45 is 5.

☛ Also Check:

GCF of 20 and 45 Examples

Example 1: Find the greatest number that divides 20 and 45 exactly.

Solution:

The greatest number that divides 20 and 45 exactly is their greatest common factor, i.e. GCF of 20 and 45.
⇒ Factors of 20 and 45:
- Factors of 20 = 1, 2, 4, 5, 10, 20
- Factors of 45 = 1, 3, 5, 9, 15, 45
Therefore, the GCF of 20 and 45 is 5.
Example 2: Find the GCF of 20 and 45, if their LCM is 180.

Solution:

∵ LCM × GCF = 20 × 45
⇒ GCF(20, 45) = (20 × 45)/180 = 5
Therefore, the greatest common factor of 20 and 45 is 5.
Example 3: For two numbers, GCF = 5 and LCM = 180. If one number is 20, find the other number.

Solution:

Given: GCF (z, 20) = 5 and LCM (z, 20) = 180
∵ GCF × LCM = 20 × (z)
⇒ z = (GCF × LCM)/20
⇒ z = (5 × 180)/20
⇒ z = 45
Therefore, the other number is 45.

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FAQs on GCF of 20 and 45

What is the GCF of 20 and 45?

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

How to Find the GCF of 20 and 45 by Long Division Method?

To find the GCF of 20, 45 using long division method, 45 is divided by 20. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

How to Find the GCF of 20 and 45 by Prime Factorization?

To find the GCF of 20 and 45, we will find the prime factorization of the given numbers, i.e. 20 = 2 × 2 × 5; 45 = 3 × 3 × 5.
⇒ Since 5 is the only common prime factor of 20 and 45. Hence, GCF (20, 45) = 5.
☛ Prime Number

What is the Relation Between LCM and GCF of 20, 45?

The following equation can be used to express the relation between LCM and GCF of 20 and 45, i.e. GCF × LCM = 20 × 45.

What are the Methods to Find GCF of 20 and 45?

There are three commonly used methods to find the GCF of 20 and 45.

By Prime Factorization
By Euclidean Algorithm
By Long Division

If the GCF of 45 and 20 is 5, Find its LCM.

GCF(45, 20) × LCM(45, 20) = 45 × 20
Since the GCF of 45 and 20 = 5
⇒ 5 × LCM(45, 20) = 900
Therefore, LCM = 180
☛ Greatest Common Factor Calculator

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