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HCF of 12 and 16

HCF of 12 and 16 is the largest possible number that divides 12 and 16 exactly without any remainder. The factors of 12 and 16 are 1, 2, 3, 4, 6, 12 and 1, 2, 4, 8, 16 respectively. There are 3 commonly used methods to find the HCF of 12 and 16 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 12 and 16
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 12 and 16?

Answer: HCF of 12 and 16 is 4.

Explanation:

The HCF of two non-zero integers, x(12) and y(16), is the highest positive integer m(4) that divides both x(12) and y(16) without any remainder.

Methods to Find HCF of 12 and 16

Let's look at the different methods for finding the HCF of 12 and 16.

Prime Factorization Method
Using Euclid's Algorithm
Listing Common Factors

HCF of 12 and 16 by Prime Factorization

Prime factorization of 12 and 16 is (2 × 2 × 3) and (2 × 2 × 2 × 2) respectively. As visible, 12 and 16 have common prime factors. Hence, the HCF of 12 and 16 is 2 × 2 = 4.

HCF of 12 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 = 12

HCF(16, 12) = HCF(12, 16 mod 12) = HCF(12, 4)
HCF(12, 4) = HCF(4, 12 mod 4) = HCF(4, 0)
HCF(4, 0) = 4 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 12 and 16 is 4.

HCF of 12 and 16 by Listing Common Factors

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 16: 1, 2, 4, 8, 16

There are 3 common factors of 12 and 16, that are 1, 2, and 4. Therefore, the highest common factor of 12 and 16 is 4.

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HCF of 12 and 16 Examples

Example 1: The product of two numbers is 192. If their HCF is 4, what is their LCM?

Solution:

Given: HCF = 4 and product of numbers = 192
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 192/4
Therefore, the LCM is 48.
Example 2: Find the highest number that divides 12 and 16 exactly.

Solution:

The highest number that divides 12 and 16 exactly is their highest common factor, i.e. HCF of 12 and 16.
⇒ Factors of 12 and 16:
- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 16 = 1, 2, 4, 8, 16
Therefore, the HCF of 12 and 16 is 4.
Example 3: Find the HCF of 12 and 16, if their LCM is 48.

Solution:

∵ LCM × HCF = 12 × 16
⇒ HCF(12, 16) = (12 × 16)/48 = 4
Therefore, the highest common factor of 12 and 16 is 4.

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FAQs on HCF of 12 and 16

What is the HCF of 12 and 16?

The HCF of 12 and 16 is 4. To calculate the Highest common factor (HCF) of 12 and 16, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 16 = 1, 2, 4, 8, 16) and choose the highest factor that exactly divides both 12 and 16, i.e., 4.

What is the Relation Between LCM and HCF of 12, 16?

The following equation can be used to express the relation between LCM and HCF of 12 and 16, i.e. HCF × LCM = 12 × 16.

If the HCF of 16 and 12 is 4, Find its LCM.

HCF(16, 12) × LCM(16, 12) = 16 × 12
Since the HCF of 16 and 12 = 4
⇒ 4 × LCM(16, 12) = 192
Therefore, LCM = 48
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What are the Methods to Find HCF of 12 and 16?

There are three commonly used methods to find the HCF of 12 and 16.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the HCF of 12 and 16 by Long Division Method?

To find the HCF of 12, 16 using long division method, 16 is divided by 12. The corresponding divisor (4) when remainder equals 0 is taken as HCF.

How to Find the HCF of 12 and 16 by Prime Factorization?

To find the HCF of 12 and 16, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 16 = 2 × 2 × 2 × 2.
⇒ Since 2, 2 are common terms in the prime factorization of 12 and 16. Hence, HCF(12, 16) = 2 × 2 = 4
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