GCF of 17 and 19
GCF of 17 and 19 is the largest possible number that divides 17 and 19 exactly without any remainder. The factors of 17 and 19 are 1, 17 and 1, 19 respectively. There are 3 commonly used methods to find the GCF of 17 and 19  Euclidean algorithm, long division, and prime factorization.
1.  GCF of 17 and 19 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 17 and 19?
Answer: GCF of 17 and 19 is 1.
Explanation:
The GCF of two nonzero integers, x(17) and y(19), is the greatest positive integer m(1) that divides both x(17) and y(19) without any remainder.
Methods to Find GCF of 17 and 19
Let's look at the different methods for finding the GCF of 17 and 19.
 Listing Common Factors
 Long Division Method
 Prime Factorization Method
GCF of 17 and 19 by Listing Common Factors
 Factors of 17: 1, 17
 Factors of 19: 1, 19
Since, 1 is the only common factor between 17 and 19. The Greatest Common Factor of 17 and 19 is 1.
GCF of 17 and 19 by Long Division
GCF of 17 and 19 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 19 (larger number) by 17 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (17) by the remainder (2).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (1) is the GCF of 17 and 19.
GCF of 17 and 19 by Prime Factorization
Prime factorization of 17 and 19 is (17) and (19) respectively. As visible, there are no common prime factors between 17 and 19, i.e. they are coprime. Hence, the GCF of 17 and 19 will be 1.
☛ Also Check:
 GCF of 72 and 36 = 36
 GCF of 3 and 12 = 3
 GCF of 24 and 64 = 8
 GCF of 45 and 63 = 9
 GCF of 20 and 50 = 10
 GCF of 56 and 84 = 28
 GCF of 16 and 20 = 4
GCF of 17 and 19 Examples

Example 1: The product of two numbers is 323. If their GCF is 1, what is their LCM?
Solution:
Given: GCF = 1 and product of numbers = 323
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 323/1
Therefore, the LCM is 323. 
Example 2: Find the GCF of 17 and 19, if their LCM is 323.
Solution:
∵ LCM × GCF = 17 × 19
⇒ GCF(17, 19) = (17 × 19)/323 = 1
Therefore, the greatest common factor of 17 and 19 is 1. 
Example 3: For two numbers, GCF = 1 and LCM = 323. If one number is 17, find the other number.
Solution:
Given: GCF (z, 17) = 1 and LCM (z, 17) = 323
∵ GCF × LCM = 17 × (z)
⇒ z = (GCF × LCM)/17
⇒ z = (1 × 323)/17
⇒ z = 19
Therefore, the other number is 19.
FAQs on GCF of 17 and 19
What is the GCF of 17 and 19?
The GCF of 17 and 19 is 1. To calculate the GCF of 17 and 19, we need to factor each number (factors of 17 = 1, 17; factors of 19 = 1, 19) and choose the greatest factor that exactly divides both 17 and 19, i.e., 1.
If the GCF of 19 and 17 is 1, Find its LCM.
GCF(19, 17) × LCM(19, 17) = 19 × 17
Since the GCF of 19 and 17 = 1
⇒ 1 × LCM(19, 17) = 323
Therefore, LCM = 323
☛ GCF Calculator
How to Find the GCF of 17 and 19 by Prime Factorization?
To find the GCF of 17 and 19, we will find the prime factorization of the given numbers, i.e. 17 = 17; 19 = 19.
⇒ There is no common prime factor for 17 and 19. Hence, GCF (17, 19) = 1.
☛ Prime Number
What are the Methods to Find GCF of 17 and 19?
There are three commonly used methods to find the GCF of 17 and 19.
 By Euclidean Algorithm
 By Long Division
 By Prime Factorization
How to Find the GCF of 17 and 19 by Long Division Method?
To find the GCF of 17, 19 using long division method, 19 is divided by 17. The corresponding divisor (1) when remainder equals 0 is taken as GCF.
What is the Relation Between LCM and GCF of 17, 19?
The following equation can be used to express the relation between LCM and GCF of 17 and 19, i.e. GCF × LCM = 17 × 19.
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