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GCF of 7 and 13

GCF of 7 and 13 is the largest possible number that divides 7 and 13 exactly without any remainder. The factors of 7 and 13 are 1, 7 and 1, 13 respectively. There are 3 commonly used methods to find the GCF of 7 and 13 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 7 and 13
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 7 and 13?

Answer: GCF of 7 and 13 is 1.

Explanation:

The GCF of two non-zero integers, x(7) and y(13), is the greatest positive integer m(1) that divides both x(7) and y(13) without any remainder.

Methods to Find GCF of 7 and 13

The methods to find the GCF of 7 and 13 are explained below.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 7 and 13 by Listing Common Factors

Factors of 7: 1, 7
Factors of 13: 1, 13

Since, 1 is the only common factor between 7 and 13. The Greatest Common Factor of 7 and 13 is 1.

GCF of 7 and 13 by Long Division

GCF of 7 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 7 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (7) by the remainder (6).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 7 and 13.

GCF of 7 and 13 by Prime Factorization

Prime factorization of 7 and 13 is (7) and (13) respectively. As visible, there are no common prime factors between 7 and 13, i.e. they are co-prime. Hence, the GCF of 7 and 13 will be 1.

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GCF of 7 and 13 Examples

Example 1: The product of two numbers is 91. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 91
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 91/1
Therefore, the LCM is 91.
Example 2: Find the greatest number that divides 7 and 13 exactly.

Solution:

The greatest number that divides 7 and 13 exactly is their greatest common factor, i.e. GCF of 7 and 13.
⇒ Factors of 7 and 13:
- Factors of 7 = 1, 7
- Factors of 13 = 1, 13
Therefore, the GCF of 7 and 13 is 1.
Example 3: For two numbers, GCF = 1 and LCM = 91. If one number is 13, find the other number.

Solution:

Given: GCF (x, 13) = 1 and LCM (x, 13) = 91
∵ GCF × LCM = 13 × (x)
⇒ x = (GCF × LCM)/13
⇒ x = (1 × 91)/13
⇒ x = 7
Therefore, the other number is 7.

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FAQs on GCF of 7 and 13

What is the GCF of 7 and 13?

The GCF of 7 and 13 is 1. To calculate the GCF of 7 and 13, we need to factor each number (factors of 7 = 1, 7; factors of 13 = 1, 13) and choose the greatest factor that exactly divides both 7 and 13, i.e., 1.

If the GCF of 13 and 7 is 1, Find its LCM.

GCF(13, 7) × LCM(13, 7) = 13 × 7
Since the GCF of 13 and 7 = 1
⇒ 1 × LCM(13, 7) = 91
Therefore, LCM = 91
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What is the Relation Between LCM and GCF of 7, 13?

The following equation can be used to express the relation between Least Common Multiple and GCF of 7 and 13, i.e. GCF × LCM = 7 × 13.

How to Find the GCF of 7 and 13 by Prime Factorization?

To find the GCF of 7 and 13, we will find the prime factorization of the given numbers, i.e. 7 = 7; 13 = 13.
⇒ There is no common prime factor for 7 and 13. Hence, GCF (7, 13) = 1.
☛ Prime Numbers

What are the Methods to Find GCF of 7 and 13?

There are three commonly used methods to find the GCF of 7 and 13.

By Listing Common Factors
By Long Division
By Prime Factorization

How to Find the GCF of 7 and 13 by Long Division Method?

To find the GCF of 7, 13 using long division method, 13 is divided by 7. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

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