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GCF of 13 and 31

GCF of 13 and 31 is the largest possible number that divides 13 and 31 exactly without any remainder. The factors of 13 and 31 are 1, 13 and 1, 31 respectively. There are 3 commonly used methods to find the GCF of 13 and 31 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 13 and 31
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 13 and 31?

Answer: GCF of 13 and 31 is 1.

Explanation:

The GCF of two non-zero integers, x(13) and y(31), is the greatest positive integer m(1) that divides both x(13) and y(31) without any remainder.

Methods to Find GCF of 13 and 31

Let's look at the different methods for finding the GCF of 13 and 31.

Long Division Method
Using Euclid's Algorithm
Prime Factorization Method

GCF of 13 and 31 by Long Division

GCF of 13 and 31 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 31 (larger number) by 13 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (13) by the remainder (5).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 13 and 31.

GCF of 13 and 31 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 = 31 and Y = 13

GCF(31, 13) = GCF(13, 31 mod 13) = GCF(13, 5)
GCF(13, 5) = GCF(5, 13 mod 5) = GCF(5, 3)
GCF(5, 3) = GCF(3, 5 mod 3) = GCF(3, 2)
GCF(3, 2) = GCF(2, 3 mod 2) = GCF(2, 1)
GCF(2, 1) = 1 (∵ GCF(X, 1) = 1)

Therefore, the value of GCF of 13 and 31 is 1.

GCF of 13 and 31 by Prime Factorization

Prime factorization of 13 and 31 is (13) and (31) respectively. As visible, there are no common prime factors between 13 and 31, i.e. they are co-prime. Hence, the GCF of 13 and 31 will be 1.

☛ Also Check:

GCF of 13 and 31 Examples

Example 1: Find the GCF of 13 and 31, if their LCM is 403.

Solution:

∵ LCM × GCF = 13 × 31
⇒ GCF(13, 31) = (13 × 31)/403 = 1
Therefore, the greatest common factor of 13 and 31 is 1.
Example 2: The product of two numbers is 403. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 403
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 403/1
Therefore, the LCM is 403.
Example 3: Find the greatest number that divides 13 and 31 exactly.

Solution:

The greatest number that divides 13 and 31 exactly is their greatest common factor, i.e. GCF of 13 and 31.
⇒ Factors of 13 and 31:
- Factors of 13 = 1, 13
- Factors of 31 = 1, 31
Therefore, the GCF of 13 and 31 is 1.

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FAQs on GCF of 13 and 31

What is the GCF of 13 and 31?

The GCF of 13 and 31 is 1. To calculate the GCF (Greatest Common Factor) of 13 and 31, we need to factor each number (factors of 13 = 1, 13; factors of 31 = 1, 31) and choose the greatest factor that exactly divides both 13 and 31, i.e., 1.

If the GCF of 31 and 13 is 1, Find its LCM.

GCF(31, 13) × LCM(31, 13) = 31 × 13
Since the GCF of 31 and 13 = 1
⇒ 1 × LCM(31, 13) = 403
Therefore, LCM = 403
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 13, 31?

The following equation can be used to express the relation between LCM and GCF of 13 and 31, i.e. GCF × LCM = 13 × 31.

How to Find the GCF of 13 and 31 by Prime Factorization?

To find the GCF of 13 and 31, we will find the prime factorization of the given numbers, i.e. 13 = 13; 31 = 31.
⇒ There is no common prime factor for 13 and 31. Hence, GCF (13, 31) = 1.
☛ Prime Numbers

How to Find the GCF of 13 and 31 by Long Division Method?

To find the GCF of 13, 31 using long division method, 31 is divided by 13. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 13 and 31?

There are three commonly used methods to find the GCF of 13 and 31.

By Euclidean Algorithm
By Prime Factorization
By Long Division

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