GCF of 52 and 68
GCF of 52 and 68 is the largest possible number that divides 52 and 68 exactly without any remainder. The factors of 52 and 68 are 1, 2, 4, 13, 26, 52 and 1, 2, 4, 17, 34, 68 respectively. There are 3 commonly used methods to find the GCF of 52 and 68  Euclidean algorithm, long division, and prime factorization.
1.  GCF of 52 and 68 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 52 and 68?
Answer: GCF of 52 and 68 is 4.
Explanation:
The GCF of two nonzero integers, x(52) and y(68), is the greatest positive integer m(4) that divides both x(52) and y(68) without any remainder.
Methods to Find GCF of 52 and 68
Let's look at the different methods for finding the GCF of 52 and 68.
 Long Division Method
 Listing Common Factors
 Prime Factorization Method
GCF of 52 and 68 by Long Division
GCF of 52 and 68 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 68 (larger number) by 52 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (52) by the remainder (16).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (4) is the GCF of 52 and 68.
GCF of 52 and 68 by Listing Common Factors
 Factors of 52: 1, 2, 4, 13, 26, 52
 Factors of 68: 1, 2, 4, 17, 34, 68
There are 3 common factors of 52 and 68, that are 1, 2, and 4. Therefore, the greatest common factor of 52 and 68 is 4.
GCF of 52 and 68 by Prime Factorization
Prime factorization of 52 and 68 is (2 × 2 × 13) and (2 × 2 × 17) respectively. As visible, 52 and 68 have common prime factors. Hence, the GCF of 52 and 68 is 2 × 2 = 4.
☛ Also Check:
 GCF of 42 and 54 = 6
 GCF of 42 and 72 = 6
 GCF of 7 and 9 = 1
 GCF of 80 and 100 = 20
 GCF of 15 and 36 = 3
 GCF of 21 and 63 = 21
 GCF of 108 and 24 = 12
GCF of 52 and 68 Examples

Example 1: For two numbers, GCF = 4 and LCM = 884. If one number is 52, find the other number.
Solution:
Given: GCF (x, 52) = 4 and LCM (x, 52) = 884
∵ GCF × LCM = 52 × (x)
⇒ x = (GCF × LCM)/52
⇒ x = (4 × 884)/52
⇒ x = 68
Therefore, the other number is 68. 
Example 2: Find the GCF of 52 and 68, if their LCM is 884.
Solution:
∵ LCM × GCF = 52 × 68
⇒ GCF(52, 68) = (52 × 68)/884 = 4
Therefore, the greatest common factor of 52 and 68 is 4. 
Example 3: The product of two numbers is 3536. If their GCF is 4, what is their LCM?
Solution:
Given: GCF = 4 and product of numbers = 3536
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 3536/4
Therefore, the LCM is 884.
FAQs on GCF of 52 and 68
What is the GCF of 52 and 68?
The GCF of 52 and 68 is 4. To calculate the greatest common factor of 52 and 68, we need to factor each number (factors of 52 = 1, 2, 4, 13, 26, 52; factors of 68 = 1, 2, 4, 17, 34, 68) and choose the greatest factor that exactly divides both 52 and 68, i.e., 4.
How to Find the GCF of 52 and 68 by Long Division Method?
To find the GCF of 52, 68 using long division method, 68 is divided by 52. The corresponding divisor (4) when remainder equals 0 is taken as GCF.
How to Find the GCF of 52 and 68 by Prime Factorization?
To find the GCF of 52 and 68, we will find the prime factorization of the given numbers, i.e. 52 = 2 × 2 × 13; 68 = 2 × 2 × 17.
⇒ Since 2, 2 are common terms in the prime factorization of 52 and 68. Hence, GCF(52, 68) = 2 × 2 = 4
☛ Prime Numbers
What are the Methods to Find GCF of 52 and 68?
There are three commonly used methods to find the GCF of 52 and 68.
 By Prime Factorization
 By Euclidean Algorithm
 By Long Division
If the GCF of 68 and 52 is 4, Find its LCM.
GCF(68, 52) × LCM(68, 52) = 68 × 52
Since the GCF of 68 and 52 = 4
⇒ 4 × LCM(68, 52) = 3536
Therefore, LCM = 884
☛ GCF Calculator
What is the Relation Between LCM and GCF of 52, 68?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 52 and 68, i.e. GCF × LCM = 52 × 68.
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