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GCF of 36 and 52

GCF of 36 and 52 is the largest possible number that divides 36 and 52 exactly without any remainder. The factors of 36 and 52 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 2, 4, 13, 26, 52 respectively. There are 3 commonly used methods to find the GCF of 36 and 52 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 36 and 52
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 36 and 52?

Answer: GCF of 36 and 52 is 4.

Explanation:

The GCF of two non-zero integers, x(36) and y(52), is the greatest positive integer m(4) that divides both x(36) and y(52) without any remainder.

Methods to Find GCF of 36 and 52

Let's look at the different methods for finding the GCF of 36 and 52.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 36 and 52 by Prime Factorization

Prime factorization of 36 and 52 is (2 × 2 × 3 × 3) and (2 × 2 × 13) respectively. As visible, 36 and 52 have common prime factors. Hence, the GCF of 36 and 52 is 2 × 2 = 4.

GCF of 36 and 52 by Listing Common Factors

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 52: 1, 2, 4, 13, 26, 52

There are 3 common factors of 36 and 52, that are 1, 2, and 4. Therefore, the greatest common factor of 36 and 52 is 4.

GCF of 36 and 52 by Long Division

GCF of 36 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 36 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (36) by the remainder (16).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 36 and 52.

☛ Also Check:

GCF of 36 and 52 Examples

Example 1: The product of two numbers is 1872. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 1872
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1872/4
Therefore, the LCM is 468.
Example 2: Find the greatest number that divides 36 and 52 exactly.

Solution:

The greatest number that divides 36 and 52 exactly is their greatest common factor, i.e. GCF of 36 and 52.
⇒ Factors of 36 and 52:
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 52 = 1, 2, 4, 13, 26, 52
Therefore, the GCF of 36 and 52 is 4.
Example 3: For two numbers, GCF = 4 and LCM = 468. If one number is 36, find the other number.

Solution:

Given: GCF (x, 36) = 4 and LCM (x, 36) = 468
∵ GCF × LCM = 36 × (x)
⇒ x = (GCF × LCM)/36
⇒ x = (4 × 468)/36
⇒ x = 52
Therefore, the other number is 52.

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FAQs on GCF of 36 and 52

What is the GCF of 36 and 52?

The GCF of 36 and 52 is 4. To calculate the GCF of 36 and 52, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 52 = 1, 2, 4, 13, 26, 52) and choose the greatest factor that exactly divides both 36 and 52, i.e., 4.

What is the Relation Between LCM and GCF of 36, 52?

The following equation can be used to express the relation between Least Common Multiple and GCF of 36 and 52, i.e. GCF × LCM = 36 × 52.

What are the Methods to Find GCF of 36 and 52?

There are three commonly used methods to find the GCF of 36 and 52.

By Prime Factorization
By Long Division
By Listing Common Factors

How to Find the GCF of 36 and 52 by Prime Factorization?

To find the GCF of 36 and 52, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 52 = 2 × 2 × 13.
⇒ Since 2, 2 are common terms in the prime factorization of 36 and 52. Hence, GCF(36, 52) = 2 × 2 = 4
☛ Prime Number

How to Find the GCF of 36 and 52 by Long Division Method?

To find the GCF of 36, 52 using long division method, 52 is divided by 36. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

If the GCF of 52 and 36 is 4, Find its LCM.

GCF(52, 36) × LCM(52, 36) = 52 × 36
Since the GCF of 52 and 36 = 4
⇒ 4 × LCM(52, 36) = 1872
Therefore, LCM = 468
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