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GCF of 12 and 13

GCF of 12 and 13 is the largest possible number that divides 12 and 13 exactly without any remainder. The factors of 12 and 13 are 1, 2, 3, 4, 6, 12 and 1, 13 respectively. There are 3 commonly used methods to find the GCF of 12 and 13 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 12 and 13
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 12 and 13?

Answer: GCF of 12 and 13 is 1.

Explanation:

The GCF of two non-zero integers, x(12) and y(13), is the greatest positive integer m(1) that divides both x(12) and y(13) without any remainder.

Methods to Find GCF of 12 and 13

The methods to find the GCF of 12 and 13 are explained below.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

GCF of 12 and 13 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 = 13 and Y = 12

GCF(13, 12) = GCF(12, 13 mod 12) = GCF(12, 1)
GCF(12, 1) = GCF(1, 12 mod 1) = GCF(1, 0)
GCF(1, 0) = 1 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 12 and 13 is 1.

GCF of 12 and 13 by Long Division

GCF of 12 and 13 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 13 (larger number) by 12 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (1).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 12 and 13.

GCF of 12 and 13 by Prime Factorization

Prime factorization of 12 and 13 is (2 × 2 × 3) and (13) respectively. As visible, there are no common prime factors between 12 and 13, i.e. they are coprime. Hence, the GCF of 12 and 13 will be 1.

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GCF of 12 and 13 Examples

Example 1: Find the greatest number that divides 12 and 13 exactly.

Solution:

The greatest number that divides 12 and 13 exactly is their greatest common factor, i.e. GCF of 12 and 13.
⇒ Factors of 12 and 13:
- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 13 = 1, 13
Therefore, the GCF of 12 and 13 is 1.
Example 2: The product of two numbers is 156. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 156
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 156/1
Therefore, the LCM is 156.
Example 3: For two numbers, GCF = 1 and LCM = 156. If one number is 12, find the other number.

Solution:

Given: GCF (z, 12) = 1 and LCM (z, 12) = 156
∵ GCF × LCM = 12 × (z)
⇒ z = (GCF × LCM)/12
⇒ z = (1 × 156)/12
⇒ z = 13
Therefore, the other number is 13.

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FAQs on GCF of 12 and 13

What is the GCF of 12 and 13?

The GCF of 12 and 13 is 1. To calculate the greatest common factor of 12 and 13, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 13 = 1, 13) and choose the greatest factor that exactly divides both 12 and 13, i.e., 1.

How to Find the GCF of 12 and 13 by Prime Factorization?

To find the GCF of 12 and 13, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 13 = 13.
⇒ There is no common prime factor for 12 and 13. Hence, GCF (12, 13) = 1.
☛ What are Prime Numbers?

What is the Relation Between LCM and GCF of 12, 13?

The following equation can be used to express the relation between LCM and GCF of 12 and 13, i.e. GCF × LCM = 12 × 13.

How to Find the GCF of 12 and 13 by Long Division Method?

To find the GCF of 12, 13 using long division method, 13 is divided by 12. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 12 and 13?

There are three commonly used methods to find the GCF of 12 and 13.

By Euclidean Algorithm
By Long Division
By Prime Factorization

If the GCF of 13 and 12 is 1, Find its LCM.

GCF(13, 12) × LCM(13, 12) = 13 × 12
Since the GCF of 13 and 12 = 1
⇒ 1 × LCM(13, 12) = 156
Therefore, LCM = 156
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