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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 non-zero 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 co-prime. Hence, the HCF of 14 and 15 will be 1.

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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.

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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
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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

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