HCF of 2 and 4

HCF of 2 and 4: HCF  (Highest Common Factor) is the highest number and can divide the given numbers without a reminder. Maths find applications in the real world but we are not aware of them. HCF finds its application in real life where you have a pile of things but want to ease the work by breaking them down. For example, you are organizing a party and have to list from 1000s to 500s or people that you are close to. This means you are going to invite the people that you are highly common with and make the list accordingly. 

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What Is the HCF of 2 and 4?

• Listing Factor Method
• Prime Factorization Method
• Division Method

Mostly all these methods follow the same steps to find the highest divisor.

HCF of 2 and 4 Using the Listing Factor Method

It is one of the easy peasy methods that could greatly work on simpler numbers or even to bigger digits if you know the factor. To find the HCF of the given numbers certain steps need to be taken.

Step 1: Find the factor of the given numbers.
Step 2: Arrange them and find the highest factor that is similar.
Step 3: The highest common factor is the HCF of the number that is given.

HCF of 2 and 4 Using the Linear Factorization Method

Let us follow the below steps and solve them.
Step 1: Find the factor of the given numbers.
The factor of 2= 1, 2
The factor of 4= 1,2,4
Step 2: Arrange them and find the similar factor.
The similar factors=1,2
Step 3: The highest common factor is the HCF of the number that is given.
The highest common factor among the similar factors =2.
Hence, HCF of (2,4)=2

HCF of 2 and 4 Using the Prime Factorization Method

Prime factorization to find HCF is a well-known method to find HCF. It works for both simple and complicated numbers. The steps to find the HCF is a little different when compared to the linear factorization method. 

Step 1: find the prime factors for the number
Step 2: find the common prime factor numbers 
Step 3: find the HCF by multiplying all the highest common prime factors.
Therefore, the HCF of 2 and 4 using the prime factorization method is as follows:

Step 1: Find the prime factors for the number
The prime factor of 2= 2
The prime factor of 4=2✕2
Step 2: Find the common prime factor numbers by multiplying them 
In this case the only common prime factor = 2
Step 3: Find the HCF by the highest common prime factors.
Hence, the HCF of (2,4)=2.

HCF of 2 and 4 Using the Long Division Method

The long division method is a complex and popularly used method to find the HCF. the steps to find the HCF using the long division method is listed below.
Step:1 Divide the highest number by the smallest one given.
Step 2: Divide the number till t reaches zero
Step3: The last divisor that divided the number to zero is the HCF of the number.
Therefore, the HCF of 2 and 4 using the long division method.

Step:1 Divide the highest number by the smallest one given.

Step 2: Divide the number till t reaches zero
For higher numbers zero is not attained in a single step hence, divide till it reaches zero.
In this case, zero is attained in a single step.
Step3: The last divisor that divided the number to zero is the HCF of the number.
The last divisor that divides 4 is 2.
Hence the HCF of (2,4)=2.

Solved Examples:

Example 1: What are the HCF and LCM of 2 and 4?
The HCF of (2,4) =  2
The LCM of (2,4) = 4

Example 2: What is the HCF of 24 and 26?
The prime factor of 24=2✕2✕2✕3
The prime factor of  26=2✕13
The HCF of (24,26) = 2

Example 3: What is the HCF of 2,4 and 6?
The factors of 2= 1,2
Factors 4= 1,2 and 4
The factors 6= 1,2,3 and 6
The HCF of (2,4,6) = 2

Example 4: Find the HCF of 28 and 46
The prime factor of 28 = 2✕2✕7
The prime factor of  46 = 2✕23
The HCF (28,46) = 2.

Example 5: What is the HCF of 2 and 4 if their LCM is 4?
The HCF of (2,4) = 2 if their LCM is 4.

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Frequently Asked Questions (FAQ)

Is the HCF of the number smaller than the LCM of the given number? 
This is because LCM is the Least Common Multiple while HCF is the highest common factor. The factors are always smaller than the multiples. Hence, the HCF of the number is smaller than the LCM of the number. 

Can I find HCF if I don’t know factorization?
Most probably No, But you can still find the HCF using prime factors or the division method. The division method will be helpful in that case but knowing the factors will save time as the name demands finding the Highest Common Factor. 

Which is the simplest way to find the HCF for small numbers?
The most simple way to find the HCF for smaller numbers is using the prime factor or factorization method.

Which method saves time to find the HCF of complex or higher numbers?
The division method helps you to save time for higher numbers.

Does HCF have any real-world applications?
Yes, HCF has applications in the real world. It helps to sort down resources, optimize the conditions, and in the schematic arrangement of things. 

What is the prime factor of 2?
The prime factor of 2 = 2

What is the HCF of 2 and 4?
The HCF of (2,4) = 2