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GCF of 65 and 100

GCF of 65 and 100 is the largest possible number that divides 65 and 100 exactly without any remainder. The factors of 65 and 100 are 1, 5, 13, 65 and 1, 2, 4, 5, 10, 20, 25, 50, 100 respectively. There are 3 commonly used methods to find the GCF of 65 and 100 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 65 and 100
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 65 and 100?

Answer: GCF of 65 and 100 is 5.

Explanation:

The GCF of two non-zero integers, x(65) and y(100), is the greatest positive integer m(5) that divides both x(65) and y(100) without any remainder.

Methods to Find GCF of 65 and 100

Let's look at the different methods for finding the GCF of 65 and 100.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 65 and 100 by Listing Common Factors

Factors of 65: 1, 5, 13, 65
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

There are 2 common factors of 65 and 100, that are 1 and 5. Therefore, the greatest common factor of 65 and 100 is 5.

GCF of 65 and 100 by Prime Factorization

Prime factorization of 65 and 100 is (5 × 13) and (2 × 2 × 5 × 5) respectively. As visible, 65 and 100 have only one common prime factor i.e. 5. Hence, the GCF of 65 and 100 is 5.

GCF of 65 and 100 by Long Division

GCF of 65 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 65 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (65) by the remainder (35).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 65 and 100.

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GCF of 65 and 100 Examples

Example 1: Find the GCF of 65 and 100, if their LCM is 1300.

Solution:

∵ LCM × GCF = 65 × 100
⇒ GCF(65, 100) = (65 × 100)/1300 = 5
Therefore, the greatest common factor of 65 and 100 is 5.
Example 2: For two numbers, GCF = 5 and LCM = 1300. If one number is 65, find the other number.

Solution:

Given: GCF (x, 65) = 5 and LCM (x, 65) = 1300
∵ GCF × LCM = 65 × (x)
⇒ x = (GCF × LCM)/65
⇒ x = (5 × 1300)/65
⇒ x = 100
Therefore, the other number is 100.
Example 3: The product of two numbers is 6500. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 6500
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 6500/5
Therefore, the LCM is 1300.

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FAQs on GCF of 65 and 100

What is the GCF of 65 and 100?

The GCF of 65 and 100 is 5. To calculate the greatest common factor (GCF) of 65 and 100, we need to factor each number (factors of 65 = 1, 5, 13, 65; factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100) and choose the greatest factor that exactly divides both 65 and 100, i.e., 5.

How to Find the GCF of 65 and 100 by Long Division Method?

To find the GCF of 65, 100 using long division method, 100 is divided by 65. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

If the GCF of 100 and 65 is 5, Find its LCM.

GCF(100, 65) × LCM(100, 65) = 100 × 65
Since the GCF of 100 and 65 = 5
⇒ 5 × LCM(100, 65) = 6500
Therefore, LCM = 1300
☛ GCF Calculator

How to Find the GCF of 65 and 100 by Prime Factorization?

To find the GCF of 65 and 100, we will find the prime factorization of the given numbers, i.e. 65 = 5 × 13; 100 = 2 × 2 × 5 × 5.
⇒ Since 5 is the only common prime factor of 65 and 100. Hence, GCF (65, 100) = 5.
☛ What is a Prime Number?

What is the Relation Between LCM and GCF of 65, 100?

The following equation can be used to express the relation between Least Common Multiple and GCF of 65 and 100, i.e. GCF × LCM = 65 × 100.

What are the Methods to Find GCF of 65 and 100?

There are three commonly used methods to find the GCF of 65 and 100.

By Long Division
By Listing Common Factors
By Prime Factorization

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