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GCF of 39 and 52

GCF of 39 and 52 is the largest possible number that divides 39 and 52 exactly without any remainder. The factors of 39 and 52 are 1, 3, 13, 39 and 1, 2, 4, 13, 26, 52 respectively. There are 3 commonly used methods to find the GCF of 39 and 52 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 39 and 52
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 39 and 52?

Answer: GCF of 39 and 52 is 13.

Explanation:

The GCF of two non-zero integers, x(39) and y(52), is the greatest positive integer m(13) that divides both x(39) and y(52) without any remainder.

Methods to Find GCF of 39 and 52

Let's look at the different methods for finding the GCF of 39 and 52.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 39 and 52 by Listing Common Factors

Factors of 39: 1, 3, 13, 39
Factors of 52: 1, 2, 4, 13, 26, 52

There are 2 common factors of 39 and 52, that are 1 and 13. Therefore, the greatest common factor of 39 and 52 is 13.

GCF of 39 and 52 by Long Division

GCF of 39 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 39 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (39) by the remainder (13).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (13) is the GCF of 39 and 52.

GCF of 39 and 52 by Prime Factorization

Prime factorization of 39 and 52 is (3 × 13) and (2 × 2 × 13) respectively. As visible, 39 and 52 have only one common prime factor i.e. 13. Hence, the GCF of 39 and 52 is 13.

☛ Also Check:

GCF of 39 and 52 Examples

Example 1: Find the greatest number that divides 39 and 52 exactly.

Solution:

The greatest number that divides 39 and 52 exactly is their greatest common factor, i.e. GCF of 39 and 52.
⇒ Factors of 39 and 52:
- Factors of 39 = 1, 3, 13, 39
- Factors of 52 = 1, 2, 4, 13, 26, 52
Therefore, the GCF of 39 and 52 is 13.
Example 2: For two numbers, GCF = 13 and LCM = 156. If one number is 39, find the other number.

Solution:

Given: GCF (y, 39) = 13 and LCM (y, 39) = 156
∵ GCF × LCM = 39 × (y)
⇒ y = (GCF × LCM)/39
⇒ y = (13 × 156)/39
⇒ y = 52
Therefore, the other number is 52.
Example 3: The product of two numbers is 2028. If their GCF is 13, what is their LCM?

Solution:

Given: GCF = 13 and product of numbers = 2028
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2028/13
Therefore, the LCM is 156.

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FAQs on GCF of 39 and 52

What is the GCF of 39 and 52?

The GCF of 39 and 52 is 13. To calculate the greatest common factor (GCF) of 39 and 52, we need to factor each number (factors of 39 = 1, 3, 13, 39; factors of 52 = 1, 2, 4, 13, 26, 52) and choose the greatest factor that exactly divides both 39 and 52, i.e., 13.

How to Find the GCF of 39 and 52 by Long Division Method?

To find the GCF of 39, 52 using long division method, 52 is divided by 39. The corresponding divisor (13) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 39 and 52?

There are three commonly used methods to find the GCF of 39 and 52.

By Euclidean Algorithm
By Long Division
By Prime Factorization

What is the Relation Between LCM and GCF of 39, 52?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 39 and 52, i.e. GCF × LCM = 39 × 52.

How to Find the GCF of 39 and 52 by Prime Factorization?

To find the GCF of 39 and 52, we will find the prime factorization of the given numbers, i.e. 39 = 3 × 13; 52 = 2 × 2 × 13.
⇒ Since 13 is the only common prime factor of 39 and 52. Hence, GCF (39, 52) = 13.
☛ What is a Prime Number?

If the GCF of 52 and 39 is 13, Find its LCM.

GCF(52, 39) × LCM(52, 39) = 52 × 39
Since the GCF of 52 and 39 = 13
⇒ 13 × LCM(52, 39) = 2028
Therefore, LCM = 156
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