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HCF of 1 and 2

HCF of 1 and 2 is the largest possible number that divides 1 and 2 exactly without any remainder. The factors of 1 and 2 are (1) and (1, 2) respectively. The commonly used methods to find the HCF of 1 and 2 are - long division, Euclidean algorithm, and listing common factors.

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

What is HCF of 1 and 2?

Answer: HCF of 1 and 2 is 1.

Explanation:

The HCF of two non-zero integers, x(1) and y(2), is the highest positive integer m(1) that divides both x(1) and y(2) without any remainder.

Methods to Find HCF of 1 and 2

The methods to find the HCF of 1 and 2 are explained below.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

HCF of 1 and 2 by Long Division

HCF of 1 and 2 is the divisor that we get when the remainder becomes 0 after doing long division.

Step 1: Divide 2 (larger number) by 1 (smaller number).
Step 2: Since the remainder = 0, the divisor (1) is the HCF of 1 and 2.

The corresponding divisor (1) is the HCF of 1 and 2.

HCF of 1 and 2 by Listing Common Factors

Factor of 1: 1
Factors of 2: 1, 2

Since 1 is the only common factor between 1 and 2. The highest common factor of 1 and 2 is 1.

HCF of 1 and 2 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 = 2 and Y = 1

HCF(2, 1) = HCF(1, 2 mod 1) = HCF(1, 0)
HCF(1, 0) = 1 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 1 and 2 is 1.

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HCF of 1 and 2 Examples

Example 1: Find the highest number that divides 1 and 2 exactly.

Solution:

The highest number that divides 1 and 2 exactly is their highest common factor, i.e. HCF of 1 and 2.
⇒ Factors of 1 and 2:
- Factors of 1 = 1
- Factors of 2 = 1, 2
Therefore, the HCF of 1 and 2 is 1.
Example 2: The product of two numbers is 2. If their HCF is 1, what is their LCM?

Solution:

Given: HCF = 1 and product of numbers = 2
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 2/1
Therefore, the LCM is 2.
Example 3: Find the HCF of 1 and 2, if their LCM is 2.

Solution:

∵ LCM × HCF = 1 × 2
⇒ HCF(1, 2) = (1 × 2)/2 = 1
Therefore, the highest common factor of 1 and 2 is 1.

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FAQs on HCF of 1 and 2

What is the HCF of 1 and 2?

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

What are the Methods to Find HCF of 1 and 2?

There are three commonly used methods to find the HCF of 1 and 2.

By Euclidean Algorithm
By Long Division
By Listing Common Factors

How to Find the HCF of 1 and 2 by Long Division Method?

To find the HCF of 1, 2 using long division method, 2 is divided by 1. The corresponding divisor (1) when remainder equals 0 is taken as HCF.

If the HCF of 2 and 1 is 1, Find its LCM.

HCF(2, 1) × LCM(2, 1) = 2 × 1
Since the HCF of 2 and 1 = 1
⇒ 1 × LCM(2, 1) = 2
Therefore, LCM = 2
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What is the Relation Between LCM and HCF of 1, 2?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 1 and 2, i.e. HCF × LCM = 1 × 2.

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