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GCF of 45 and 90

GCF of 45 and 90 is the largest possible number that divides 45 and 90 exactly without any remainder. The factors of 45 and 90 are 1, 3, 5, 9, 15, 45 and 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 respectively. There are 3 commonly used methods to find the GCF of 45 and 90 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 45 and 90
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 45 and 90?

Answer: GCF of 45 and 90 is 45.

Explanation:

The GCF of two non-zero integers, x(45) and y(90), is the greatest positive integer m(45) that divides both x(45) and y(90) without any remainder.

Methods to Find GCF of 45 and 90

Let's look at the different methods for finding the GCF of 45 and 90.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 45 and 90 by Listing Common Factors

Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

There are 6 common factors of 45 and 90, that are 1, 3, 5, 9, 45, and 15. Therefore, the greatest common factor of 45 and 90 is 45.

GCF of 45 and 90 by Prime Factorization

Prime factorization of 45 and 90 is (3 × 3 × 5) and (2 × 3 × 3 × 5) respectively. As visible, 45 and 90 have common prime factors. Hence, the GCF of 45 and 90 is 3 × 3 × 5 = 45.

GCF of 45 and 90 by Long Division

GCF of 45 and 90 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 90 (larger number) by 45 (smaller number).
Step 2: Since the remainder = 0, the divisor (45) is the GCF of 45 and 90.

The corresponding divisor (45) is the GCF of 45 and 90.

☛ Also Check:

GCF of 45 and 90 Examples

Example 1: For two numbers, GCF = 45 and LCM = 90. If one number is 45, find the other number.

Solution:

Given: GCF (z, 45) = 45 and LCM (z, 45) = 90
∵ GCF × LCM = 45 × (z)
⇒ z = (GCF × LCM)/45
⇒ z = (45 × 90)/45
⇒ z = 90
Therefore, the other number is 90.
Example 2: Find the greatest number that divides 45 and 90 exactly.

Solution:

The greatest number that divides 45 and 90 exactly is their greatest common factor, i.e. GCF of 45 and 90.
⇒ Factors of 45 and 90:
- Factors of 45 = 1, 3, 5, 9, 15, 45
- Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Therefore, the GCF of 45 and 90 is 45.
Example 3: Find the GCF of 45 and 90, if their LCM is 90.

Solution:

∵ LCM × GCF = 45 × 90
⇒ GCF(45, 90) = (45 × 90)/90 = 45
Therefore, the greatest common factor of 45 and 90 is 45.

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FAQs on GCF of 45 and 90

What is the GCF of 45 and 90?

The GCF of 45 and 90 is 45. To calculate the greatest common factor of 45 and 90, we need to factor each number (factors of 45 = 1, 3, 5, 9, 15, 45; factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90) and choose the greatest factor that exactly divides both 45 and 90, i.e., 45.

If the GCF of 90 and 45 is 45, Find its LCM.

GCF(90, 45) × LCM(90, 45) = 90 × 45
Since the GCF of 90 and 45 = 45
⇒ 45 × LCM(90, 45) = 4050
Therefore, LCM = 90
☛ GCF Calculator

How to Find the GCF of 45 and 90 by Long Division Method?

To find the GCF of 45, 90 using long division method, 90 is divided by 45. The corresponding divisor (45) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 45 and 90?

There are three commonly used methods to find the GCF of 45 and 90.

By Long Division
By Prime Factorization
By Euclidean Algorithm

How to Find the GCF of 45 and 90 by Prime Factorization?

To find the GCF of 45 and 90, we will find the prime factorization of the given numbers, i.e. 45 = 3 × 3 × 5; 90 = 2 × 3 × 3 × 5.
⇒ Since 3, 3, 5 are common terms in the prime factorization of 45 and 90. Hence, GCF(45, 90) = 3 × 3 × 5 = 45
☛ Prime Number

What is the Relation Between LCM and GCF of 45, 90?

The following equation can be used to express the relation between Least Common Multiple and GCF of 45 and 90, i.e. GCF × LCM = 45 × 90.

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