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GCF of 100 and 150

GCF of 100 and 150 is the largest possible number that divides 100 and 150 exactly without any remainder. The factors of 100 and 150 are 1, 2, 4, 5, 10, 20, 25, 50, 100 and 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150 respectively. There are 3 commonly used methods to find the GCF of 100 and 150 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 100 and 150
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 100 and 150?

Answer: GCF of 100 and 150 is 50.

Explanation:

The GCF of two non-zero integers, x(100) and y(150), is the greatest positive integer m(50) that divides both x(100) and y(150) without any remainder.

Methods to Find GCF of 100 and 150

The methods to find the GCF of 100 and 150 are explained below.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 100 and 150 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 = 150 and Y = 100

GCF(150, 100) = GCF(100, 150 mod 100) = GCF(100, 50)
GCF(100, 50) = GCF(50, 100 mod 50) = GCF(50, 0)
GCF(50, 0) = 50 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 100 and 150 is 50.

GCF of 100 and 150 by Long Division

GCF of 100 and 150 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 150 (larger number) by 100 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (100) by the remainder (50).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (50) is the GCF of 100 and 150.

GCF of 100 and 150 by Listing Common Factors

Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

There are 6 common factors of 100 and 150, that are 1, 2, 5, 10, 50, and 25. Therefore, the greatest common factor of 100 and 150 is 50.

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GCF of 100 and 150 Examples

Example 1: Find the greatest number that divides 100 and 150 exactly.

Solution:

The greatest number that divides 100 and 150 exactly is their greatest common factor, i.e. GCF of 100 and 150.
⇒ Factors of 100 and 150:
- Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100
- Factors of 150 = 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Therefore, the GCF of 100 and 150 is 50.
Example 2: For two numbers, GCF = 50 and LCM = 300. If one number is 150, find the other number.

Solution:

Given: GCF (y, 150) = 50 and LCM (y, 150) = 300
∵ GCF × LCM = 150 × (y)
⇒ y = (GCF × LCM)/150
⇒ y = (50 × 300)/150
⇒ y = 100
Therefore, the other number is 100.
Example 3: The product of two numbers is 15000. If their GCF is 50, what is their LCM?

Solution:

Given: GCF = 50 and product of numbers = 15000
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 15000/50
Therefore, the LCM is 300.

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FAQs on GCF of 100 and 150

What is the GCF of 100 and 150?

The GCF of 100 and 150 is 50. To calculate the GCF of 100 and 150, we need to factor each number (factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100; factors of 150 = 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150) and choose the greatest factor that exactly divides both 100 and 150, i.e., 50.

If the GCF of 150 and 100 is 50, Find its LCM.

GCF(150, 100) × LCM(150, 100) = 150 × 100
Since the GCF of 150 and 100 = 50
⇒ 50 × LCM(150, 100) = 15000
Therefore, LCM = 300
☛ GCF Calculator

What are the Methods to Find GCF of 100 and 150?

There are three commonly used methods to find the GCF of 100 and 150.

By Euclidean Algorithm
By Long Division
By Prime Factorization

What is the Relation Between LCM and GCF of 100, 150?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 100 and 150, i.e. GCF × LCM = 100 × 150.

How to Find the GCF of 100 and 150 by Prime Factorization?

To find the GCF of 100 and 150, we will find the prime factorization of the given numbers, i.e. 100 = 2 × 2 × 5 × 5; 150 = 2 × 3 × 5 × 5.
⇒ Since 2, 5, 5 are common terms in the prime factorization of 100 and 150. Hence, GCF(100, 150) = 2 × 5 × 5 = 50
☛ Prime Numbers

How to Find the GCF of 100 and 150 by Long Division Method?

To find the GCF of 100, 150 using long division method, 150 is divided by 100. The corresponding divisor (50) when remainder equals 0 is taken as GCF.

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