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GCF of 13 and 52

GCF of 13 and 52 is the largest possible number that divides 13 and 52 exactly without any remainder. The factors of 13 and 52 are 1, 13 and 1, 2, 4, 13, 26, 52 respectively. There are 3 commonly used methods to find the GCF of 13 and 52 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 13 and 52
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 13 and 52?

Answer: GCF of 13 and 52 is 13.

Explanation:

The GCF of two non-zero integers, x(13) and y(52), is the greatest positive integer m(13) that divides both x(13) and y(52) without any remainder.

Methods to Find GCF of 13 and 52

Let's look at the different methods for finding the GCF of 13 and 52.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 13 and 52 by Prime Factorization

Prime factorization of 13 and 52 is (13) and (2 × 2 × 13) respectively. As visible, 13 and 52 have only one common prime factor i.e. 13. Hence, the GCF of 13 and 52 is 13.

GCF of 13 and 52 by Listing Common Factors

Factors of 13: 1, 13
Factors of 52: 1, 2, 4, 13, 26, 52

There are 2 common factors of 13 and 52, that are 1 and 13. Therefore, the greatest common factor of 13 and 52 is 13.

GCF of 13 and 52 by Long Division

GCF of 13 and 52 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 52 (larger number) by 13 (smaller number).
Step 2: Since the remainder = 0, the divisor (13) is the GCF of 13 and 52.

The corresponding divisor (13) is the GCF of 13 and 52.

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GCF of 13 and 52 Examples

Example 1: Find the greatest number that divides 13 and 52 exactly.

Solution:

The greatest number that divides 13 and 52 exactly is their greatest common factor, i.e. GCF of 13 and 52.
⇒ Factors of 13 and 52:
- Factors of 13 = 1, 13
- Factors of 52 = 1, 2, 4, 13, 26, 52
Therefore, the GCF of 13 and 52 is 13.
Example 2: The product of two numbers is 676. If their GCF is 13, what is their LCM?

Solution:

Given: GCF = 13 and product of numbers = 676
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 676/13
Therefore, the LCM is 52.
Example 3: Find the GCF of 13 and 52, if their LCM is 52.

Solution:

∵ LCM × GCF = 13 × 52
⇒ GCF(13, 52) = (13 × 52)/52 = 13
Therefore, the greatest common factor of 13 and 52 is 13.

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FAQs on GCF of 13 and 52

What is the GCF of 13 and 52?

The GCF of 13 and 52 is 13. To calculate the GCF of 13 and 52, we need to factor each number (factors of 13 = 1, 13; factors of 52 = 1, 2, 4, 13, 26, 52) and choose the greatest factor that exactly divides both 13 and 52, i.e., 13.

What is the Relation Between LCM and GCF of 13, 52?

The following equation can be used to express the relation between LCM and GCF of 13 and 52, i.e. GCF × LCM = 13 × 52.

If the GCF of 52 and 13 is 13, Find its LCM.

GCF(52, 13) × LCM(52, 13) = 52 × 13
Since the GCF of 52 and 13 = 13
⇒ 13 × LCM(52, 13) = 676
Therefore, LCM = 52
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 13 and 52?

There are three commonly used methods to find the GCF of 13 and 52.

By Listing Common Factors
By Long Division
By Prime Factorization

How to Find the GCF of 13 and 52 by Long Division Method?

To find the GCF of 13, 52 using long division method, 52 is divided by 13. The corresponding divisor (13) when remainder equals 0 is taken as GCF.

How to Find the GCF of 13 and 52 by Prime Factorization?

To find the GCF of 13 and 52, we will find the prime factorization of the given numbers, i.e. 13 = 13; 52 = 2 × 2 × 13.
⇒ Since 13 is the only common prime factor of 13 and 52. Hence, GCF (13, 52) = 13.
☛ What is a Prime Number?

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