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HCF of 8 and 16

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

1.	HCF of 8 and 16
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 8 and 16?

Answer: HCF of 8 and 16 is 8.

Explanation:

The HCF of two non-zero integers, x(8) and y(16), is the highest positive integer m(8) that divides both x(8) and y(16) without any remainder.

Methods to Find HCF of 8 and 16

Let's look at the different methods for finding the HCF of 8 and 16.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

HCF of 8 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 = 8

HCF(16, 8) = HCF(8, 16 mod 8) = HCF(8, 0)
HCF(8, 0) = 8 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 8 and 16 is 8.

HCF of 8 and 16 by Prime Factorization

Prime factorization of 8 and 16 is (2 × 2 × 2) and (2 × 2 × 2 × 2) respectively. As visible, 8 and 16 have common prime factors. Hence, the HCF of 8 and 16 is 2 × 2 × 2 = 8.

HCF of 8 and 16 by Long Division

HCF of 8 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 8 (smaller number).
Step 2: Since the remainder = 0, the divisor (8) is the HCF of 8 and 16.

The corresponding divisor (8) is the HCF of 8 and 16.

☛ Also Check:

HCF of 8 and 16 Examples

Example 1: Find the HCF of 8 and 16, if their LCM is 16.

Solution:

∵ LCM × HCF = 8 × 16
⇒ HCF(8, 16) = (8 × 16)/16 = 8
Therefore, the highest common factor of 8 and 16 is 8.
Example 2: The product of two numbers is 128. If their HCF is 8, what is their LCM?

Solution:

Given: HCF = 8 and product of numbers = 128
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 128/8
Therefore, the LCM is 16.
Example 3: For two numbers, HCF = 8 and LCM = 16. If one number is 16, find the other number.

Solution:

Given: HCF (x, 16) = 8 and LCM (x, 16) = 16
∵ HCF × LCM = 16 × (x)
⇒ x = (HCF × LCM)/16
⇒ x = (8 × 16)/16
⇒ x = 8
Therefore, the other number is 8.

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FAQs on HCF of 8 and 16

What is the HCF of 8 and 16?

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

How to Find the HCF of 8 and 16 by Long Division Method?

To find the HCF of 8, 16 using long division method, 16 is divided by 8. The corresponding divisor (8) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 8, 16?

The following equation can be used to express the relation between Least Common Multiple and HCF of 8 and 16, i.e. HCF × LCM = 8 × 16.

What are the Methods to Find HCF of 8 and 16?

There are three commonly used methods to find the HCF of 8 and 16.

By Long Division
By Prime Factorization
By Euclidean Algorithm

If the HCF of 16 and 8 is 8, Find its LCM.

HCF(16, 8) × LCM(16, 8) = 16 × 8
Since the HCF of 16 and 8 = 8
⇒ 8 × LCM(16, 8) = 128
Therefore, LCM = 16
☛ Highest Common Factor Calculator

How to Find the HCF of 8 and 16 by Prime Factorization?

To find the HCF of 8 and 16, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 16 = 2 × 2 × 2 × 2.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 8 and 16. Hence, HCF(8, 16) = 2 × 2 × 2 = 8
☛ What is a Prime Number?

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