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HCF of 1 and 3

HCF of 1 and 3 is the largest possible number that divides 1 and 3 exactly without any remainder. The factors of 1 and 3 are (1) and (1, 3) respectively. There are 3 commonly used methods to find the HCF of 1 and 3 - listing common factors, Euclidean algorithm, and long division.

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

What is HCF of 1 and 3?

Answer: HCF of 1 and 3 is 1.

Explanation:

The HCF of two non-zero integers, x(1) and y(3), is the highest positive integer m(1) that divides both x(1) and y(3) without any remainder.

Methods to Find HCF of 1 and 3

Let's look at the different methods for finding the HCF of 1 and 3.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

HCF of 1 and 3 by Long Division

HCF of 1 and 3 is the divisor that we get when the remainder becomes 0 after doing long division.

Step 1: Divide 3 (larger number) by 1 (smaller number).
Step 2: Since the remainder = 0, the divisor (1) is the HCF of 1 and 3.

The corresponding divisor (1) is the HCF of 1 and 3.

HCF of 1 and 3 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 = 3 and Y = 1

HCF(3, 1) = HCF(1, 3 mod 1) = HCF(1, 0)
HCF(1, 0) = 1 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 1 and 3 is 1.

HCF of 1 and 3 by Listing Common Factors

Factor of 1: 1
Factors of 3: 1, 3

Since 1 is the only common factor between 1 and 3. The highest common factor of 1 and 3 is 1.

☛ Also Check:

HCF of 1 and 3 Examples

Example 1: For two numbers, HCF = 1 and LCM = 3. If one number is 3, find the other number.

Solution:

Given: HCF (z, 3) = 1 and LCM (z, 3) = 3
∵ HCF × LCM = 3 × (z)
⇒ z = (HCF × LCM)/3
⇒ z = (1 × 3)/3
⇒ z = 1
Therefore, the other number is 1.
Example 2: Find the HCF of 1 and 3, if their LCM is 3.

Solution:

∵ LCM × HCF = 1 × 3
⇒ HCF(1, 3) = (1 × 3)/3 = 1
Therefore, the highest common factor of 1 and 3 is 1.
Example 3: The product of two numbers is 3. If their HCF is 1, what is their LCM?

Solution:

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

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FAQs on HCF of 1 and 3

What is the HCF of 1 and 3?

The HCF of 1 and 3 is 1. To calculate the HCF of 1 and 3, we need to factor each number (factor of 1 = 1; factors of 3 = 1, 3) and choose the highest factor that exactly divides both 1 and 3, i.e., 1.

How to Find the HCF of 1 and 3 by Long Division Method?

To find the HCF of 1, 3 using long division method, 3 is divided by 1. The corresponding divisor (1) when remainder equals 0 is taken as HCF.

If the HCF of 3 and 1 is 1, Find its LCM.

HCF(3, 1) × LCM(3, 1) = 3 × 1
Since the HCF of 3 and 1 = 1
⇒ 1 × LCM(3, 1) = 3
Therefore, LCM = 3
☛ Highest Common Factor Calculator

What are the Methods to Find HCF of 1 and 3?

There are three commonly used methods to find the HCF of 1 and 3.

By Long Division
By Euclidean Algorithm
By Listing Common Factors

What is the Relation Between LCM and HCF of 1, 3?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 1 and 3, i.e. HCF × LCM = 1 × 3.

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