HCF of 2 and 5

HCF of 2 and 5 is the largest possible number that divides 2 and 5 exactly without any remainder. The factors of 2 and 5 are 1, 2 and 1, 5 respectively. There are 3 commonly used methods to find the HCF of 2 and 5 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 2 and 5
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 2 and 5?

Answer: HCF of 2 and 5 is 1.

Explanation:

The HCF of two non-zero integers, x(2) and y(5), is the highest positive integer m(1) that divides both x(2) and y(5) without any remainder.

Methods to Find HCF of 2 and 5

The methods to find the HCF of 2 and 5 are explained below.

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

HCF of 2 and 5 by Listing Common Factors

Factors of 2: 1, 2
Factors of 5: 1, 5

Since, 1 is the only common factor between 2 and 5. The highest common factor of 2 and 5 is 1.

HCF of 2 and 5 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 = 5 and Y = 2

HCF(5, 2) = HCF(2, 5 mod 2) = HCF(2, 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 2 and 5 is 1.

HCF of 2 and 5 by Long Division

HCF of 2 and 5 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 5 (larger number) by 2 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (2) by the remainder (1).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the HCF of 2 and 5.

☛ Also Check:

HCF of 2 and 5 Examples

Example 1: For two numbers, HCF = 1 and LCM = 10. If one number is 5, find the other number.

Solution:

Given: HCF (y, 5) = 1 and LCM (y, 5) = 10
∵ HCF × LCM = 5 × (y)
⇒ y = (HCF × LCM)/5
⇒ y = (1 × 10)/5
⇒ y = 2
Therefore, the other number is 2.
Example 2: Find the highest number that divides 2 and 5 exactly.

Solution:

The highest number that divides 2 and 5 exactly is their highest common factor, i.e. HCF of 2 and 5.
⇒ Factors of 2 and 5:
- Factors of 2 = 1, 2
- Factors of 5 = 1, 5
Therefore, the HCF of 2 and 5 is 1.
Example 3: The product of two numbers is 10. If their HCF is 1, what is their LCM?

Solution:

Given: HCF = 1 and product of numbers = 10
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 10/1
Therefore, the LCM is 10.

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FAQs on HCF of 2 and 5

What is the HCF of 2 and 5?

The HCF of 2 and 5 is 1. To calculate the Highest common factor of 2 and 5, we need to factor each number (factors of 2 = 1, 2; factors of 5 = 1, 5) and choose the highest factor that exactly divides both 2 and 5, i.e., 1.

How to Find the HCF of 2 and 5 by Prime Factorization?

To find the HCF of 2 and 5, we will find the prime factorization of the given numbers, i.e. 2 = 2; 5 = 5.
⇒ There is no common prime factor for 2 and 5. Hence, HCF (2, 5) = 1.
☛ Prime Number

What are the Methods to Find HCF of 2 and 5?

There are three commonly used methods to find the HCF of 2 and 5.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the HCF of 2 and 5 by Long Division Method?

To find the HCF of 2, 5 using long division method, 5 is divided by 2. The corresponding divisor (1) when remainder equals 0 is taken as HCF.

If the HCF of 5 and 2 is 1, Find its LCM.

HCF(5, 2) × LCM(5, 2) = 5 × 2
Since the HCF of 5 and 2 = 1
⇒ 1 × LCM(5, 2) = 10
Therefore, LCM = 10
☛ Highest Common Factor Calculator

What is the Relation Between LCM and HCF of 2, 5?

The following equation can be used to express the relation between LCM and HCF of 2 and 5, i.e. HCF × LCM = 2 × 5.

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