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GCF of 40 and 50

GCF of 40 and 50 is the largest possible number that divides 40 and 50 exactly without any remainder. The factors of 40 and 50 are 1, 2, 4, 5, 8, 10, 20, 40 and 1, 2, 5, 10, 25, 50 respectively. There are 3 commonly used methods to find the GCF of 40 and 50 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 40 and 50
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 40 and 50?

Answer: GCF of 40 and 50 is 10.

Explanation:

The GCF of two non-zero integers, x(40) and y(50), is the greatest positive integer m(10) that divides both x(40) and y(50) without any remainder.

Methods to Find GCF of 40 and 50

Let's look at the different methods for finding the GCF of 40 and 50.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 40 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 = 40

GCF(50, 40) = GCF(40, 50 mod 40) = GCF(40, 10)
GCF(40, 10) = GCF(10, 40 mod 10) = GCF(10, 0)
GCF(10, 0) = 10 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 40 and 50 is 10.

GCF of 40 and 50 by Long Division

GCF of 40 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 40 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (40) by the remainder (10).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (10) is the GCF of 40 and 50.

GCF of 40 and 50 by Listing Common Factors

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Factors of 50: 1, 2, 5, 10, 25, 50

There are 4 common factors of 40 and 50, that are 1, 2, 10, and 5. Therefore, the greatest common factor of 40 and 50 is 10.

☛ Also Check:

GCF of 40 and 50 Examples

Example 1: Find the GCF of 40 and 50, if their LCM is 200.

Solution:

∵ LCM × GCF = 40 × 50
⇒ GCF(40, 50) = (40 × 50)/200 = 10
Therefore, the greatest common factor of 40 and 50 is 10.
Example 2: Find the greatest number that divides 40 and 50 exactly.

Solution:

The greatest number that divides 40 and 50 exactly is their greatest common factor, i.e. GCF of 40 and 50.
⇒ Factors of 40 and 50:
- Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
- Factors of 50 = 1, 2, 5, 10, 25, 50
Therefore, the GCF of 40 and 50 is 10.
Example 3: For two numbers, GCF = 10 and LCM = 200. If one number is 50, find the other number.

Solution:

Given: GCF (x, 50) = 10 and LCM (x, 50) = 200
∵ GCF × LCM = 50 × (x)
⇒ x = (GCF × LCM)/50
⇒ x = (10 × 200)/50
⇒ x = 40
Therefore, the other number is 40.

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FAQs on GCF of 40 and 50

What is the GCF of 40 and 50?

The GCF of 40 and 50 is 10. To calculate the GCF of 40 and 50, we need to factor each number (factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40; factors of 50 = 1, 2, 5, 10, 25, 50) and choose the greatest factor that exactly divides both 40 and 50, i.e., 10.

How to Find the GCF of 40 and 50 by Long Division Method?

To find the GCF of 40, 50 using long division method, 50 is divided by 40. The corresponding divisor (10) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 40 and 50?

There are three commonly used methods to find the GCF of 40 and 50.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the GCF of 40 and 50 by Prime Factorization?

To find the GCF of 40 and 50, we will find the prime factorization of the given numbers, i.e. 40 = 2 × 2 × 2 × 5; 50 = 2 × 5 × 5.
⇒ Since 2, 5 are common terms in the prime factorization of 40 and 50. Hence, GCF(40, 50) = 2 × 5 = 10
☛ Prime Number

If the GCF of 50 and 40 is 10, Find its LCM.

GCF(50, 40) × LCM(50, 40) = 50 × 40
Since the GCF of 50 and 40 = 10
⇒ 10 × LCM(50, 40) = 2000
Therefore, LCM = 200
☛ GCF Calculator

What is the Relation Between LCM and GCF of 40, 50?

The following equation can be used to express the relation between LCM and GCF of 40 and 50, i.e. GCF × LCM = 40 × 50.

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