### HCF of 4 and 6

**HCF of 4 and 6**: HCF is the highest common factor that can divide any given number equally. The HCF of the number can be a factor or prime factor or divisor. The HCF is also known as Greatest Common Measure (GCM) or Greatest Common Divisor (GCD).

There are three methods to find the HCF of the number:

- Listing Factor Method
- Long Division Method
- Prime Factorization Method.

Each method has its own steps to get the HCF of the number.

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**HCF of 4 and 6 Using the Prime Factorization Method**

The prime factorization mainly involves the prime number. The steps to find the HCF using prime factorization are as follows:

Step 1: Find the prime factor of each number and take the common prime factors

Step 2: Multiply the common prime factors which are the HCF of the given number.**Therefore, the HCF of 4 and 6 using prime factorization is as follows: **

Step 1: Find the prime factor of each number and take the common prime factors

The prime factor of 4 = 2×2

The prime factor of 6 = 2×3

Step 2: Multiply the common prime factors which are the HCF of the given number.

The only common prime number is 2, Hence we don’t need to multiply.

Therefore, **HCF (4,6) = 2**

**HCF of 4 and 6 Using the Listing Factor Method**

The steps that are followed to find the HCF of the number using the listing factor method are described below:

Step 1: Find the factors and list the common factors

Step 2: The highest common factor is the one with a similar factor which is a larger number.**Therefore, the HCF of 4 and 6 using the listing factor method is as follows: **

Step 1: Find the factors and list the common factors

The factor of 4 = 1,2,4

The factor of 6 = 1,2,3 and 6

There are two common factors for 4 and 6 they are 1 and 2.

Step 2: The highest common factor is the one with a similar factor which is a larger number.

The highest common factor is 2.

Hence **HCF(4,6) = 2.**

**HCF of 4 and 6 Using the Long Division Method**

The following steps that are explained below are used to find the HCF using the long division method.

Step 1: The larger number is divided by the smaller number.

Step 2: The divisor which brings zero is the HCF of the number**Therefore, the HCF of 4 and 6 using the long division method is as** **follows: **

Step 1: The larger number is divided by the smaller number.

Step 2: The divisor which brings zero is the HCF of the number

The last divisor to bring zero is 2

Hence**, HCF(4,6) = 2**

**Solved Examples**

**Example 1: find the HCF of 11 and 22**

The HCF (12,22) = 11.

**Example 2: what is the Greatest common divisor of 4 and 6?**

The greatest common divisor of 4 and 6 = 2

**Example 3: There are two numbers whose LCM and HCF are given find another number****LCM of the number = 12****HCF of the number = 2****The number given = 4**

HCF (x, 4) = 2

LCM(x,4) = 12

Therefore, LCM×HCF = 4 × (X)

X = (LCM × HCF) ∕ 4

Hence,

X = (2× 12) ∕ 4

Therefore, X = 6 is the other number.

**Example 4: If the product of two numbers is 24 and their HCF is 2. Find their LCM?**

LCM×HCF = product of two numbers

LCM = product of two numbers ∕ HCF

LCM = 24 ∕ 2

Hence LCM = 12.

**Example 5: Find the HCF of 616 and 32 using the prime factorization method.**

The prime factor of 4 = 2×2

The prime factor of 6 = 2×3

HCF (4,6) = 2.

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**Frequently Asked Question (FAQ):**

**What is the GCD of 616 and 32?**

GCD (616,32) = 8

**What is the LCM of 4 and 6 if their HCF is 2?**

The LCM (4,6) = 12

**Solve 4 and 6 and find their HCF using the division method**

HCF(4,6) = 2

**What is the product of 4 and 6?**

The product of 4 and 6 = 24

**What are the common factors in 4 and 6?**

There are two common factors for 4 and 6 they are 1 and 2.

**What is the HCF of 4 and 6 if their LCM is 12?**

The HCF(4,6) = 2.

**Is HCF and GCD the same?**

Yes, HCF and GCD are the same.

Written by

Prerit Jain