HCF of 17 and 19
HCF 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 HCF of 17 and 19  prime factorization, Euclidean algorithm, and long division.
1.  HCF of 17 and 19 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 17 and 19?
Answer: HCF of 17 and 19 is 1.
Explanation:
The HCF of two nonzero integers, x(17) and y(19), is the highest positive integer m(1) that divides both x(17) and y(19) without any remainder.
Methods to Find HCF of 17 and 19
Let's look at the different methods for finding the HCF of 17 and 19.
 Prime Factorization Method
 Listing Common Factors
 Using Euclid's Algorithm
HCF 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 HCF of 17 and 19 will be 1.
HCF 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 highest common factor of 17 and 19 is 1.
HCF of 17 and 19 by Euclidean Algorithm
As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.
Here X = 19 and Y = 17
 HCF(19, 17) = HCF(17, 19 mod 17) = HCF(17, 2)
 HCF(17, 2) = HCF(2, 17 mod 2) = HCF(2, 1)
 HCF(2, 1) = 1 (∵ HCF(X, 1) = 1)
Therefore, the value of HCF of 17 and 19 is 1.
☛ Also Check:
 HCF of 398, 436 and 542 = 2
 HCF of 120, 144 and 204 = 12
 HCF of 391 and 667 = 23
 HCF of 441, 567 and 693 = 63
 HCF of 8, 10 and 12 = 2
 HCF of 408 and 1032 = 24
 HCF of 404 and 96 = 4
HCF of 17 and 19 Examples

Example 1: The product of two numbers is 323. If their HCF is 1, what is their LCM?
Solution:
Given: HCF = 1 and product of numbers = 323
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 323/1
Therefore, the LCM is 323. 
Example 2: For two numbers, HCF = 1 and LCM = 323. If one number is 17, find the other number.
Solution:
Given: HCF (y, 17) = 1 and LCM (y, 17) = 323
∵ HCF × LCM = 17 × (y)
⇒ y = (HCF × LCM)/17
⇒ y = (1 × 323)/17
⇒ y = 19
Therefore, the other number is 19. 
Example 3: Find the highest number that divides 17 and 19 exactly.
Solution:
The highest number that divides 17 and 19 exactly is their highest common factor, i.e. HCF of 17 and 19.
⇒ Factors of 17 and 19: Factors of 17 = 1, 17
 Factors of 19 = 1, 19
Therefore, the HCF of 17 and 19 is 1.
FAQs on HCF of 17 and 19
What is the HCF of 17 and 19?
The HCF of 17 and 19 is 1. To calculate the Highest common factor of 17 and 19, we need to factor each number (factors of 17 = 1, 17; factors of 19 = 1, 19) and choose the highest factor that exactly divides both 17 and 19, i.e., 1.
What is the Relation Between LCM and HCF of 17, 19?
The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 17 and 19, i.e. HCF × LCM = 17 × 19.
How to Find the HCF of 17 and 19 by Prime Factorization?
To find the HCF 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, HCF (17, 19) = 1.
☛ Prime Numbers
If the HCF of 19 and 17 is 1, Find its LCM.
HCF(19, 17) × LCM(19, 17) = 19 × 17
Since the HCF of 19 and 17 = 1
⇒ 1 × LCM(19, 17) = 323
Therefore, LCM = 323
☛ HCF Calculator
How to Find the HCF of 17 and 19 by Long Division Method?
To find the HCF of 17, 19 using long division method, 19 is divided by 17. The corresponding divisor (1) when remainder equals 0 is taken as HCF.
What are the Methods to Find HCF of 17 and 19?
There are three commonly used methods to find the HCF of 17 and 19.
 By Prime Factorization
 By Euclidean Algorithm
 By Long Division
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