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HCF of 14 and 16

HCF of 14 and 16 is the largest possible number that divides 14 and 16 exactly without any remainder. The factors of 14 and 16 are 1, 2, 7, 14 and 1, 2, 4, 8, 16 respectively. There are 3 commonly used methods to find the HCF of 14 and 16 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 14 and 16
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 14 and 16?

Answer: HCF of 14 and 16 is 2.

Explanation:

The HCF of two non-zero integers, x(14) and y(16), is the highest positive integer m(2) that divides both x(14) and y(16) without any remainder.

Methods to Find HCF of 14 and 16

Let's look at the different methods for finding the HCF of 14 and 16.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

HCF of 14 and 16 by Prime Factorization

Prime factorization of 14 and 16 is (2 × 7) and (2 × 2 × 2 × 2) respectively. As visible, 14 and 16 have only one common prime factor i.e. 2. Hence, the HCF of 14 and 16 is 2.

HCF of 14 and 16 by Long Division

HCF of 14 and 16 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 16 (larger number) by 14 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (14) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the HCF of 14 and 16.

HCF of 14 and 16 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 = 16 and Y = 14

HCF(16, 14) = HCF(14, 16 mod 14) = HCF(14, 2)
HCF(14, 2) = HCF(2, 14 mod 2) = HCF(2, 0)
HCF(2, 0) = 2 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 14 and 16 is 2.

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HCF of 14 and 16 Examples

Example 1: Find the HCF of 14 and 16, if their LCM is 112.

Solution:

∵ LCM × HCF = 14 × 16
⇒ HCF(14, 16) = (14 × 16)/112 = 2
Therefore, the highest common factor of 14 and 16 is 2.
Example 2: The product of two numbers is 224. If their HCF is 2, what is their LCM?

Solution:

Given: HCF = 2 and product of numbers = 224
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 224/2
Therefore, the LCM is 112.
Example 3: Find the highest number that divides 14 and 16 exactly.

Solution:

The highest number that divides 14 and 16 exactly is their highest common factor, i.e. HCF of 14 and 16.
⇒ Factors of 14 and 16:
- Factors of 14 = 1, 2, 7, 14
- Factors of 16 = 1, 2, 4, 8, 16
Therefore, the HCF of 14 and 16 is 2.

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FAQs on HCF of 14 and 16

What is the HCF of 14 and 16?

The HCF of 14 and 16 is 2. To calculate the Highest common factor of 14 and 16, we need to factor each number (factors of 14 = 1, 2, 7, 14; factors of 16 = 1, 2, 4, 8, 16) and choose the highest factor that exactly divides both 14 and 16, i.e., 2.

What are the Methods to Find HCF of 14 and 16?

There are three commonly used methods to find the HCF of 14 and 16.

By Long Division
By Prime Factorization
By Euclidean Algorithm

If the HCF of 16 and 14 is 2, Find its LCM.

HCF(16, 14) × LCM(16, 14) = 16 × 14
Since the HCF of 16 and 14 = 2
⇒ 2 × LCM(16, 14) = 224
Therefore, LCM = 112
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How to Find the HCF of 14 and 16 by Long Division Method?

To find the HCF of 14, 16 using long division method, 16 is divided by 14. The corresponding divisor (2) when remainder equals 0 is taken as HCF.

How to Find the HCF of 14 and 16 by Prime Factorization?

To find the HCF of 14 and 16, we will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 16 = 2 × 2 × 2 × 2.
⇒ Since 2 is the only common prime factor of 14 and 16. Hence, HCF (14, 16) = 2.
☛ Prime Number

What is the Relation Between LCM and HCF of 14, 16?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 14 and 16, i.e. HCF × LCM = 14 × 16.

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