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HCF of 4 and 12

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

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

What is HCF of 4 and 12?

Answer: HCF of 4 and 12 is 4.

Explanation:

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

Methods to Find HCF of 4 and 12

Let's look at the different methods for finding the HCF of 4 and 12.

Long Division Method
Listing Common Factors
Prime Factorization Method

HCF of 4 and 12 by Long Division

HCF of 4 and 12 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 12 (larger number) by 4 (smaller number).
Step 2: Since the remainder = 0, the divisor (4) is the HCF of 4 and 12.

The corresponding divisor (4) is the HCF of 4 and 12.

HCF of 4 and 12 by Listing Common Factors

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

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

HCF of 4 and 12 by Prime Factorization

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

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HCF of 4 and 12 Examples

Example 1: Find the highest number that divides 4 and 12 exactly.

Solution:

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

Solution:

∵ LCM × HCF = 4 × 12
⇒ HCF(4, 12) = (4 × 12)/12 = 4
Therefore, the highest common factor of 4 and 12 is 4.
Example 3: The product of two numbers is 48. If their HCF is 4, what is their LCM?

Solution:

Given: HCF = 4 and product of numbers = 48
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 48/4
Therefore, the LCM is 12.

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FAQs on HCF of 4 and 12

What is the HCF of 4 and 12?

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

How to Find the HCF of 4 and 12 by Prime Factorization?

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

What are the Methods to Find HCF of 4 and 12?

There are three commonly used methods to find the HCF of 4 and 12.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the HCF of 4 and 12 by Long Division Method?

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

What is the Relation Between LCM and HCF of 4, 12?

The following equation can be used to express the relation between LCM and HCF of 4 and 12, i.e. HCF × LCM = 4 × 12.

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

HCF(12, 4) × LCM(12, 4) = 12 × 4
Since the HCF of 12 and 4 = 4
⇒ 4 × LCM(12, 4) = 48
Therefore, LCM = 12
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