A day full of math games & activities. Find one near you.

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 non-zero 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 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.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

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.

Download FREE Study Materials

HCF and LCM

Math worksheets and
visual curriculum