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GCF of 45 and 50

GCF of 45 and 50 is the largest possible number that divides 45 and 50 exactly without any remainder. The factors of 45 and 50 are 1, 3, 5, 9, 15, 45 and 1, 2, 5, 10, 25, 50 respectively. There are 3 commonly used methods to find the GCF of 45 and 50 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 45 and 50
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 45 and 50?

Answer: GCF of 45 and 50 is 5.

Explanation:

The GCF of two non-zero integers, x(45) and y(50), is the greatest positive integer m(5) that divides both x(45) and y(50) without any remainder.

Methods to Find GCF of 45 and 50

The methods to find the GCF of 45 and 50 are explained below.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

GCF of 45 and 50 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 = 50 and Y = 45

GCF(50, 45) = GCF(45, 50 mod 45) = GCF(45, 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 45 and 50 is 5.

GCF of 45 and 50 by Prime Factorization

Prime factorization of 45 and 50 is (3 × 3 × 5) and (2 × 5 × 5) respectively. As visible, 45 and 50 have only one common prime factor i.e. 5. Hence, the GCF of 45 and 50 is 5.

GCF of 45 and 50 by Long Division

GCF of 45 and 50 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 50 (larger number) by 45 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (45) by the remainder (5).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 45 and 50.

☛ Also Check:

GCF of 45 and 50 Examples

Example 1: The product of two numbers is 2250. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 2250
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2250/5
Therefore, the LCM is 450.
Example 2: For two numbers, GCF = 5 and LCM = 450. If one number is 50, find the other number.

Solution:

Given: GCF (z, 50) = 5 and LCM (z, 50) = 450
∵ GCF × LCM = 50 × (z)
⇒ z = (GCF × LCM)/50
⇒ z = (5 × 450)/50
⇒ z = 45
Therefore, the other number is 45.
Example 3: Find the GCF of 45 and 50, if their LCM is 450.

Solution:

∵ LCM × GCF = 45 × 50
⇒ GCF(45, 50) = (45 × 50)/450 = 5
Therefore, the greatest common factor of 45 and 50 is 5.

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FAQs on GCF of 45 and 50

What is the GCF of 45 and 50?

The GCF of 45 and 50 is 5. To calculate the greatest common factor (GCF) of 45 and 50, we need to factor each number (factors of 45 = 1, 3, 5, 9, 15, 45; factors of 50 = 1, 2, 5, 10, 25, 50) and choose the greatest factor that exactly divides both 45 and 50, i.e., 5.

What are the Methods to Find GCF of 45 and 50?

There are three commonly used methods to find the GCF of 45 and 50.

By Long Division
By Listing Common Factors
By Prime Factorization

What is the Relation Between LCM and GCF of 45, 50?

The following equation can be used to express the relation between Least Common Multiple and GCF of 45 and 50, i.e. GCF × LCM = 45 × 50.

If the GCF of 50 and 45 is 5, Find its LCM.

GCF(50, 45) × LCM(50, 45) = 50 × 45
Since the GCF of 50 and 45 = 5
⇒ 5 × LCM(50, 45) = 2250
Therefore, LCM = 450
☛ Greatest Common Factor Calculator

How to Find the GCF of 45 and 50 by Prime Factorization?

To find the GCF of 45 and 50, we will find the prime factorization of the given numbers, i.e. 45 = 3 × 3 × 5; 50 = 2 × 5 × 5.
⇒ Since 5 is the only common prime factor of 45 and 50. Hence, GCF (45, 50) = 5.
☛ Prime Numbers

How to Find the GCF of 45 and 50 by Long Division Method?

To find the GCF of 45, 50 using long division method, 50 is divided by 45. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

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