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HCF of 4 and 6

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

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

What is HCF of 4 and 6?

Answer: HCF of 4 and 6 is 2.

Explanation:

The HCF of two non-zero integers, x(4) and y(6), is the highest positive integer m(2) that divides both x(4) and y(6) without any remainder.

Methods to Find HCF of 4 and 6

The methods to find the HCF of 4 and 6 are explained below.

Long Division Method
Listing Common Factors
Prime Factorization Method

HCF of 4 and 6 by Long Division

HCF of 4 and 6 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

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

The corresponding divisor (2) is the HCF of 4 and 6.

HCF of 4 and 6 by Listing Common Factors

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

There are 2 common factors of 4 and 6, that are 1 and 2. Therefore, the highest common factor of 4 and 6 is 2.

HCF of 4 and 6 by Prime Factorization

Prime factorization of 4 and 6 is (2 × 2) and (2 × 3) respectively. As visible, 4 and 6 have only one common prime factor i.e. 2. Hence, the HCF of 4 and 6 is 2.

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HCF of 4 and 6 Examples

Example 1: The product of two numbers is 24. If their HCF is 2, what is their LCM?

Solution:

Given: HCF = 2 and product of numbers = 24
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 24/2
Therefore, the LCM is 12.
Example 2: Find the HCF of 4 and 6, if their LCM is 12.

Solution:

∵ LCM × HCF = 4 × 6
⇒ HCF(4, 6) = (4 × 6)/12 = 2
Therefore, the highest common factor of 4 and 6 is 2.
Example 3: For two numbers, HCF = 2 and LCM = 12. If one number is 4, find the other number.

Solution:

Given: HCF (y, 4) = 2 and LCM (y, 4) = 12
∵ HCF × LCM = 4 × (y)
⇒ y = (HCF × LCM)/4
⇒ y = (2 × 12)/4
⇒ y = 6
Therefore, the other number is 6.

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FAQs on HCF of 4 and 6

What is the HCF of 4 and 6?

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

What are the Methods to Find HCF of 4 and 6?

There are three commonly used methods to find the HCF of 4 and 6.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the HCF of 4 and 6 by Prime Factorization?

To find the HCF of 4 and 6, we will find the prime factorization of the given numbers, i.e. 4 = 2 × 2; 6 = 2 × 3.
⇒ Since 2 is the only common prime factor of 4 and 6. Hence, HCF (4, 6) = 2.
☛ What are Prime Numbers?

What is the Relation Between LCM and HCF of 4, 6?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 4 and 6, i.e. HCF × LCM = 4 × 6.

If the HCF of 6 and 4 is 2, Find its LCM.

HCF(6, 4) × LCM(6, 4) = 6 × 4
Since the HCF of 6 and 4 = 2
⇒ 2 × LCM(6, 4) = 24
Therefore, LCM = 12
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How to Find the HCF of 4 and 6 by Long Division Method?

To find the HCF of 4, 6 using long division method, 6 is divided by 4. The corresponding divisor (2) when remainder equals 0 is taken as HCF.

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