HCF of 2 and 12
HCF of 2 and 12 is the largest possible number that divides 2 and 12 exactly without any remainder. The factors of 2 and 12 are 1, 2 and 1, 2, 3, 4, 6, 12 respectively. There are 3 commonly used methods to find the HCF of 2 and 12  prime factorization, Euclidean algorithm, and long division.
1.  HCF of 2 and 12 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 2 and 12?
Answer: HCF of 2 and 12 is 2.
Explanation:
The HCF of two nonzero integers, x(2) and y(12), is the highest positive integer m(2) that divides both x(2) and y(12) without any remainder.
Methods to Find HCF of 2 and 12
Let's look at the different methods for finding the HCF of 2 and 12.
 Prime Factorization Method
 Using Euclid's Algorithm
 Long Division Method
HCF of 2 and 12 by Prime Factorization
Prime factorization of 2 and 12 is (2) and (2 × 2 × 3) respectively. As visible, 2 and 12 have only one common prime factor i.e. 2. Hence, the HCF of 2 and 12 is 2.
HCF of 2 and 12 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 = 12 and Y = 2
 HCF(12, 2) = HCF(2, 12 mod 2) = HCF(2, 0)
 HCF(2, 0) = 2 (∵ HCF(X, 0) = X, where X ≠ 0)
Therefore, the value of HCF of 2 and 12 is 2.
HCF of 2 and 12 by Long Division
HCF of 2 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 2 (smaller number).
 Step 2: Since the remainder = 0, the divisor (2) is the HCF of 2 and 12.
The corresponding divisor (2) is the HCF of 2 and 12.
☛ Also Check:
 HCF of 8 and 12 = 4
 HCF of 1 and 2 = 1
 HCF of 90 and 105 = 15
 HCF of 5 and 10 = 5
 HCF of 106, 159 and 265 = 53
 HCF of 3 and 4 = 1
 HCF of 60 and 75 = 15
HCF of 2 and 12 Examples

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

Example 2: Find the HCF of 2 and 12, if their LCM is 12.
Solution:
∵ LCM × HCF = 2 × 12
⇒ HCF(2, 12) = (2 × 12)/12 = 2
Therefore, the highest common factor of 2 and 12 is 2. 
Example 3: 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.
FAQs on HCF of 2 and 12
What is the HCF of 2 and 12?
The HCF of 2 and 12 is 2. To calculate the HCF (Highest Common Factor) of 2 and 12, we need to factor each number (factors of 2 = 1, 2; factors of 12 = 1, 2, 3, 4, 6, 12) and choose the highest factor that exactly divides both 2 and 12, i.e., 2.
What are the Methods to Find HCF of 2 and 12?
There are three commonly used methods to find the HCF of 2 and 12.
 By Long Division
 By Prime Factorization
 By Euclidean Algorithm
What is the Relation Between LCM and HCF of 2, 12?
The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 2 and 12, i.e. HCF × LCM = 2 × 12.
If the HCF of 12 and 2 is 2, Find its LCM.
HCF(12, 2) × LCM(12, 2) = 12 × 2
Since the HCF of 12 and 2 = 2
⇒ 2 × LCM(12, 2) = 24
Therefore, LCM = 12
☛ HCF Calculator
How to Find the HCF of 2 and 12 by Prime Factorization?
To find the HCF of 2 and 12, we will find the prime factorization of the given numbers, i.e. 2 = 2; 12 = 2 × 2 × 3.
⇒ Since 2 is the only common prime factor of 2 and 12. Hence, HCF (2, 12) = 2.
☛ What is a Prime Number?
How to Find the HCF of 2 and 12 by Long Division Method?
To find the HCF of 2, 12 using long division method, 12 is divided by 2. The corresponding divisor (2) when remainder equals 0 is taken as HCF.
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