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GCF of 8 and 52

GCF of 8 and 52 is the largest possible number that divides 8 and 52 exactly without any remainder. The factors of 8 and 52 are 1, 2, 4, 8 and 1, 2, 4, 13, 26, 52 respectively. There are 3 commonly used methods to find the GCF of 8 and 52 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 8 and 52
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 8 and 52?

Answer: GCF of 8 and 52 is 4.

Explanation:

The GCF of two non-zero integers, x(8) and y(52), is the greatest positive integer m(4) that divides both x(8) and y(52) without any remainder.

Methods to Find GCF of 8 and 52

The methods to find the GCF of 8 and 52 are explained below.

Prime Factorization Method
Using Euclid's Algorithm
Long Division Method

GCF of 8 and 52 by Prime Factorization

Prime factorization of 8 and 52 is (2 × 2 × 2) and (2 × 2 × 13) respectively. As visible, 8 and 52 have common prime factors. Hence, the GCF of 8 and 52 is 2 × 2 = 4.

GCF of 8 and 52 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 = 52 and Y = 8

GCF(52, 8) = GCF(8, 52 mod 8) = GCF(8, 4)
GCF(8, 4) = GCF(4, 8 mod 4) = GCF(4, 0)
GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 8 and 52 is 4.

GCF of 8 and 52 by Long Division

GCF of 8 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 8 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (8) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 8 and 52.

☛ Also Check:

GCF of 8 and 52 Examples

Example 1: The product of two numbers is 416. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 416
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 416/4
Therefore, the LCM is 104.
Example 2: Find the GCF of 8 and 52, if their LCM is 104.

Solution:

∵ LCM × GCF = 8 × 52
⇒ GCF(8, 52) = (8 × 52)/104 = 4
Therefore, the greatest common factor of 8 and 52 is 4.
Example 3: Find the greatest number that divides 8 and 52 exactly.

Solution:

The greatest number that divides 8 and 52 exactly is their greatest common factor, i.e. GCF of 8 and 52.
⇒ Factors of 8 and 52:
- Factors of 8 = 1, 2, 4, 8
- Factors of 52 = 1, 2, 4, 13, 26, 52
Therefore, the GCF of 8 and 52 is 4.

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FAQs on GCF of 8 and 52

What is the GCF of 8 and 52?

The GCF of 8 and 52 is 4. To calculate the greatest common factor (GCF) of 8 and 52, we need to factor each number (factors of 8 = 1, 2, 4, 8; factors of 52 = 1, 2, 4, 13, 26, 52) and choose the greatest factor that exactly divides both 8 and 52, i.e., 4.

How to Find the GCF of 8 and 52 by Prime Factorization?

To find the GCF of 8 and 52, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 52 = 2 × 2 × 13.
⇒ Since 2, 2 are common terms in the prime factorization of 8 and 52. Hence, GCF(8, 52) = 2 × 2 = 4
☛ What are Prime Numbers?

If the GCF of 52 and 8 is 4, Find its LCM.

GCF(52, 8) × LCM(52, 8) = 52 × 8
Since the GCF of 52 and 8 = 4
⇒ 4 × LCM(52, 8) = 416
Therefore, LCM = 104
☛ GCF Calculator

What are the Methods to Find GCF of 8 and 52?

There are three commonly used methods to find the GCF of 8 and 52.

By Euclidean Algorithm
By Prime Factorization
By Long Division

What is the Relation Between LCM and GCF of 8, 52?

The following equation can be used to express the relation between LCM and GCF of 8 and 52, i.e. GCF × LCM = 8 × 52.

How to Find the GCF of 8 and 52 by Long Division Method?

To find the GCF of 8, 52 using long division method, 52 is divided by 8. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

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