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GCF of 15 and 100

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

1.	GCF of 15 and 100
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 15 and 100?

Answer: GCF of 15 and 100 is 5.

Explanation:

The GCF of two non-zero integers, x(15) and y(100), is the greatest positive integer m(5) that divides both x(15) and y(100) without any remainder.

Methods to Find GCF of 15 and 100

Let's look at the different methods for finding the GCF of 15 and 100.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 15 and 100 by Long Division

GCF of 15 and 100 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 100 (larger number) by 15 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (15) by the remainder (10).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 15 and 100.

GCF of 15 and 100 by Listing Common Factors

Factors of 15: 1, 3, 5, 15
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

There are 2 common factors of 15 and 100, that are 1 and 5. Therefore, the greatest common factor of 15 and 100 is 5.

GCF of 15 and 100 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 = 100 and Y = 15

GCF(100, 15) = GCF(15, 100 mod 15) = GCF(15, 10)
GCF(15, 10) = GCF(10, 15 mod 10) = GCF(10, 5)
GCF(10, 5) = GCF(5, 10 mod 5) = GCF(5, 0)
GCF(5, 0) = 5 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 15 and 100 is 5.

☛ Also Check:

GCF of 15 and 100 Examples

Example 1: The product of two numbers is 1500. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 1500
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1500/5
Therefore, the LCM is 300.
Example 2: For two numbers, GCF = 5 and LCM = 300. If one number is 100, find the other number.

Solution:

Given: GCF (y, 100) = 5 and LCM (y, 100) = 300
∵ GCF × LCM = 100 × (y)
⇒ y = (GCF × LCM)/100
⇒ y = (5 × 300)/100
⇒ y = 15
Therefore, the other number is 15.
Example 3: Find the GCF of 15 and 100, if their LCM is 300.

Solution:

∵ LCM × GCF = 15 × 100
⇒ GCF(15, 100) = (15 × 100)/300 = 5
Therefore, the greatest common factor of 15 and 100 is 5.

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FAQs on GCF of 15 and 100

What is the GCF of 15 and 100?

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

What is the Relation Between LCM and GCF of 15, 100?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 15 and 100, i.e. GCF × LCM = 15 × 100.

How to Find the GCF of 15 and 100 by Prime Factorization?

To find the GCF of 15 and 100, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 100 = 2 × 2 × 5 × 5.
⇒ Since 5 is the only common prime factor of 15 and 100. Hence, GCF (15, 100) = 5.
☛ Prime Number

How to Find the GCF of 15 and 100 by Long Division Method?

To find the GCF of 15, 100 using long division method, 100 is divided by 15. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 15 and 100?

There are three commonly used methods to find the GCF of 15 and 100.

By Long Division
By Prime Factorization
By Listing Common Factors

If the GCF of 100 and 15 is 5, Find its LCM.

GCF(100, 15) × LCM(100, 15) = 100 × 15
Since the GCF of 100 and 15 = 5
⇒ 5 × LCM(100, 15) = 1500
Therefore, LCM = 300
☛ Greatest Common Factor Calculator

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