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HCF of 6 and 16

HCF of 6 and 16 is the largest possible number that divides 6 and 16 exactly without any remainder. The factors of 6 and 16 are 1, 2, 3, 6 and 1, 2, 4, 8, 16 respectively. There are 3 commonly used methods to find the HCF of 6 and 16 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 6 and 16
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 6 and 16?

Answer: HCF of 6 and 16 is 2.

Explanation:

The HCF of two non-zero integers, x(6) and y(16), is the highest positive integer m(2) that divides both x(6) and y(16) without any remainder.

Methods to Find HCF of 6 and 16

The methods to find the HCF of 6 and 16 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

HCF of 6 and 16 by Prime Factorization

Prime factorization of 6 and 16 is (2 × 3) and (2 × 2 × 2 × 2) respectively. As visible, 6 and 16 have only one common prime factor i.e. 2. Hence, the HCF of 6 and 16 is 2.

HCF of 6 and 16 by Listing Common Factors

Factors of 6: 1, 2, 3, 6
Factors of 16: 1, 2, 4, 8, 16

There are 2 common factors of 6 and 16, that are 1 and 2. Therefore, the highest common factor of 6 and 16 is 2.

HCF of 6 and 16 by Long Division

HCF of 6 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 6 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (6) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the HCF of 6 and 16.

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HCF of 6 and 16 Examples

Example 1: Find the HCF of 6 and 16, if their LCM is 48.

Solution:

∵ LCM × HCF = 6 × 16
⇒ HCF(6, 16) = (6 × 16)/48 = 2
Therefore, the highest common factor of 6 and 16 is 2.
Example 2: For two numbers, HCF = 2 and LCM = 48. If one number is 6, find the other number.

Solution:

Given: HCF (x, 6) = 2 and LCM (x, 6) = 48
∵ HCF × LCM = 6 × (x)
⇒ x = (HCF × LCM)/6
⇒ x = (2 × 48)/6
⇒ x = 16
Therefore, the other number is 16.
Example 3: Find the highest number that divides 6 and 16 exactly.

Solution:

The highest number that divides 6 and 16 exactly is their highest common factor, i.e. HCF of 6 and 16.
⇒ Factors of 6 and 16:
- Factors of 6 = 1, 2, 3, 6
- Factors of 16 = 1, 2, 4, 8, 16
Therefore, the HCF of 6 and 16 is 2.

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FAQs on HCF of 6 and 16

What is the HCF of 6 and 16?

The HCF of 6 and 16 is 2. To calculate the Highest common factor (HCF) of 6 and 16, we need to factor each number (factors of 6 = 1, 2, 3, 6; factors of 16 = 1, 2, 4, 8, 16) and choose the highest factor that exactly divides both 6 and 16, i.e., 2.

How to Find the HCF of 6 and 16 by Prime Factorization?

To find the HCF of 6 and 16, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 16 = 2 × 2 × 2 × 2.
⇒ Since 2 is the only common prime factor of 6 and 16. Hence, HCF (6, 16) = 2.
☛ What are Prime Numbers?

How to Find the HCF of 6 and 16 by Long Division Method?

To find the HCF of 6, 16 using long division method, 16 is divided by 6. The corresponding divisor (2) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 6 and 16?

There are three commonly used methods to find the HCF of 6 and 16.

By Euclidean Algorithm
By Long Division
By Prime Factorization

If the HCF of 16 and 6 is 2, Find its LCM.

HCF(16, 6) × LCM(16, 6) = 16 × 6
Since the HCF of 16 and 6 = 2
⇒ 2 × LCM(16, 6) = 96
Therefore, LCM = 48
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What is the Relation Between LCM and HCF of 6, 16?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 6 and 16, i.e. HCF × LCM = 6 × 16.

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