HCF of 14 and 15
HCF of 14 and 15 is the largest possible number that divides 14 and 15 exactly without any remainder. The factors of 14 and 15 are 1, 2, 7, 14 and 1, 3, 5, 15 respectively. There are 3 commonly used methods to find the HCF of 14 and 15  Euclidean algorithm, long division, and prime factorization.
1.  HCF of 14 and 15 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 14 and 15?
Answer: HCF of 14 and 15 is 1.
Explanation:
The HCF of two nonzero integers, x(14) and y(15), is the highest positive integer m(1) that divides both x(14) and y(15) without any remainder.
Methods to Find HCF of 14 and 15
Let's look at the different methods for finding the HCF of 14 and 15.
 Long Division Method
 Listing Common Factors
 Prime Factorization Method
HCF of 14 and 15 by Long Division
HCF of 14 and 15 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 15 (larger number) by 14 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (14) by the remainder (1).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (1) is the HCF of 14 and 15.
HCF of 14 and 15 by Listing Common Factors
 Factors of 14: 1, 2, 7, 14
 Factors of 15: 1, 3, 5, 15
Since, 1 is the only common factor between 14 and 15. The highest common factor of 14 and 15 is 1.
HCF of 14 and 15 by Prime Factorization
Prime factorization of 14 and 15 is (2 × 7) and (3 × 5) respectively. As visible, there are no common prime factors between 14 and 15, i.e. they are coprime. Hence, the HCF of 14 and 15 will be 1.
☛ Also Check:
 HCF of 20, 30 and 40 = 10
 HCF of 403, 434 and 465 = 31
 HCF of 24, 36 and 40 = 4
 HCF of 49 and 56 = 7
 HCF of 120 and 150 = 30
 HCF of 3 and 5 = 1
 HCF of 12, 45 and 75 = 3
HCF of 14 and 15 Examples

Example 1: Find the HCF of 14 and 15, if their LCM is 210.
Solution:
∵ LCM × HCF = 14 × 15
⇒ HCF(14, 15) = (14 × 15)/210 = 1
Therefore, the highest common factor of 14 and 15 is 1. 
Example 2: The product of two numbers is 210. If their HCF is 1, what is their LCM?
Solution:
Given: HCF = 1 and product of numbers = 210
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 210/1
Therefore, the LCM is 210. 
Example 3: For two numbers, HCF = 1 and LCM = 210. If one number is 15, find the other number.
Solution:
Given: HCF (z, 15) = 1 and LCM (z, 15) = 210
∵ HCF × LCM = 15 × (z)
⇒ z = (HCF × LCM)/15
⇒ z = (1 × 210)/15
⇒ z = 14
Therefore, the other number is 14.
FAQs on HCF of 14 and 15
What is the HCF of 14 and 15?
The HCF of 14 and 15 is 1. To calculate the HCF (Highest Common Factor) of 14 and 15, we need to factor each number (factors of 14 = 1, 2, 7, 14; factors of 15 = 1, 3, 5, 15) and choose the highest factor that exactly divides both 14 and 15, i.e., 1.
How to Find the HCF of 14 and 15 by Prime Factorization?
To find the HCF of 14 and 15, we will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 15 = 3 × 5.
⇒ There is no common prime factor for 14 and 15. Hence, HCF (14, 15) = 1.
☛ What are Prime Numbers?
How to Find the HCF of 14 and 15 by Long Division Method?
To find the HCF of 14, 15 using long division method, 15 is divided by 14. The corresponding divisor (1) when remainder equals 0 is taken as HCF.
What is the Relation Between LCM and HCF of 14, 15?
The following equation can be used to express the relation between Least Common Multiple and HCF of 14 and 15, i.e. HCF × LCM = 14 × 15.
If the HCF of 15 and 14 is 1, Find its LCM.
HCF(15, 14) × LCM(15, 14) = 15 × 14
Since the HCF of 15 and 14 = 1
⇒ 1 × LCM(15, 14) = 210
Therefore, LCM = 210
☛ HCF Calculator
What are the Methods to Find HCF of 14 and 15?
There are three commonly used methods to find the HCF of 14 and 15.
 By Prime Factorization
 By Long Division
 By Listing Common Factors
visual curriculum