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 14 and 35 = 7
- GCF of 20 and 40 = 20
- GCF of 24 and 48 = 24
- GCF of 4 and 10 = 2
- GCF of 9 and 30 = 3
- GCF of 28 and 84 = 28
- GCF of 36 and 100 = 4
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.
