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GCF of 13 and 20

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

1.	GCF of 13 and 20
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 13 and 20?

Answer: GCF of 13 and 20 is 1.

Explanation:

The GCF of two non-zero integers, x(13) and y(20), is the greatest positive integer m(1) that divides both x(13) and y(20) without any remainder.

Methods to Find GCF of 13 and 20

Let's look at the different methods for finding the GCF of 13 and 20.

Long Division Method
Using Euclid's Algorithm
Prime Factorization Method

GCF of 13 and 20 by Long Division

GCF of 13 and 20 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 20 (larger number) by 13 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (13) by the remainder (7).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 13 and 20.

GCF of 13 and 20 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 = 20 and Y = 13

GCF(20, 13) = GCF(13, 20 mod 13) = GCF(13, 7)
GCF(13, 7) = GCF(7, 13 mod 7) = GCF(7, 6)
GCF(7, 6) = GCF(6, 7 mod 6) = GCF(6, 1)
GCF(6, 1) = 1 (∵ GCF(X, 1) = 1)

Therefore, the value of GCF of 13 and 20 is 1.

GCF of 13 and 20 by Prime Factorization

Prime factorization of 13 and 20 is (13) and (2 × 2 × 5) respectively. As visible, there are no common prime factors between 13 and 20, i.e. they are coprime. Hence, the GCF of 13 and 20 will be 1.

☛ Also Check:

GCF of 13 and 20 Examples

Example 1: Find the greatest number that divides 13 and 20 exactly.

Solution:

The greatest number that divides 13 and 20 exactly is their greatest common factor, i.e. GCF of 13 and 20.
⇒ Factors of 13 and 20:
- Factors of 13 = 1, 13
- Factors of 20 = 1, 2, 4, 5, 10, 20
Therefore, the GCF of 13 and 20 is 1.
Example 2: For two numbers, GCF = 1 and LCM = 260. If one number is 13, find the other number.

Solution:

Given: GCF (y, 13) = 1 and LCM (y, 13) = 260
∵ GCF × LCM = 13 × (y)
⇒ y = (GCF × LCM)/13
⇒ y = (1 × 260)/13
⇒ y = 20
Therefore, the other number is 20.
Example 3: The product of two numbers is 260. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 260
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 260/1
Therefore, the LCM is 260.

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FAQs on GCF of 13 and 20

What is the GCF of 13 and 20?

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

How to Find the GCF of 13 and 20 by Long Division Method?

To find the GCF of 13, 20 using long division method, 20 is divided by 13. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 13, 20?

The following equation can be used to express the relation between LCM and GCF of 13 and 20, i.e. GCF × LCM = 13 × 20.

What are the Methods to Find GCF of 13 and 20?

There are three commonly used methods to find the GCF of 13 and 20.

By Prime Factorization
By Listing Common Factors
By Long Division

How to Find the GCF of 13 and 20 by Prime Factorization?

To find the GCF of 13 and 20, we will find the prime factorization of the given numbers, i.e. 13 = 13; 20 = 2 × 2 × 5.
⇒ There is no common prime factor for 13 and 20. Hence, GCF (13, 20) = 1.
☛ Prime Numbers

If the GCF of 20 and 13 is 1, Find its LCM.

GCF(20, 13) × LCM(20, 13) = 20 × 13
Since the GCF of 20 and 13 = 1
⇒ 1 × LCM(20, 13) = 260
Therefore, LCM = 260
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