HCF of 2 and 9

HCF of 2 and 9 is the largest possible number that divides 2 and 9 exactly without any remainder. The factors of 2 and 9 are 1, 2 and 1, 3, 9 respectively. There are 3 commonly used methods to find the HCF of 2 and 9 - long division, prime factorization, and Euclidean algorithm.

1.	HCF of 2 and 9
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 2 and 9?

Answer: HCF of 2 and 9 is 1.

Explanation:

The HCF of two non-zero integers, x(2) and y(9), is the highest positive integer m(1) that divides both x(2) and y(9) without any remainder.

Methods to Find HCF of 2 and 9

Let's look at the different methods for finding the HCF of 2 and 9.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

HCF of 2 and 9 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 = 9 and Y = 2

HCF(9, 2) = HCF(2, 9 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 9 is 1.

HCF of 2 and 9 by Prime Factorization

Prime factorization of 2 and 9 is (2) and (3 × 3) respectively. As visible, there are no common prime factors between 2 and 9, i.e. they are co-prime. Hence, the HCF of 2 and 9 will be 1.

HCF of 2 and 9 by Long Division

HCF of 2 and 9 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 9 (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 9.

☛ Also Check:

Example 1: For two numbers, HCF = 1 and LCM = 18. If one number is 2, find the other number.

Solution:

Given: HCF (z, 2) = 1 and LCM (z, 2) = 18
∵ HCF × LCM = 2 × (z)
⇒ z = (HCF × LCM)/2
⇒ z = (1 × 18)/2
⇒ z = 9
Therefore, the other number is 9.
Example 2: The product of two numbers is 18. If their HCF is 1, what is their LCM?

Solution:

Given: HCF = 1 and product of numbers = 18
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 18/1
Therefore, the LCM is 18.
Example 3: Find the highest number that divides 2 and 9 exactly.

Solution:

The highest number that divides 2 and 9 exactly is their highest common factor, i.e. HCF of 2 and 9.
⇒ Factors of 2 and 9:
- Factors of 2 = 1, 2
- Factors of 9 = 1, 3, 9
Therefore, the HCF of 2 and 9 is 1.

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FAQs on HCF of 2 and 9

What is the HCF of 2 and 9?

The HCF of 2 and 9 is 1. To calculate the HCF of 2 and 9, we need to factor each number (factors of 2 = 1, 2; factors of 9 = 1, 3, 9) and choose the highest factor that exactly divides both 2 and 9, i.e., 1.

What is the Relation Between LCM and HCF of 2, 9?

The following equation can be used to express the relation between Least Common Multiple and HCF of 2 and 9, i.e. HCF × LCM = 2 × 9.

What are the Methods to Find HCF of 2 and 9?

There are three commonly used methods to find the HCF of 2 and 9.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the HCF of 2 and 9 by Prime Factorization?

To find the HCF of 2 and 9, we will find the prime factorization of the given numbers, i.e. 2 = 2; 9 = 3 × 3.
⇒ There is no common prime factor for 2 and 9. Hence, HCF (2, 9) = 1.
☛ What is a Prime Number?

How to Find the HCF of 2 and 9 by Long Division Method?

To find the HCF of 2, 9 using long division method, 9 is divided by 2. The corresponding divisor (1) when remainder equals 0 is taken as HCF.

If the HCF of 9 and 2 is 1, Find its LCM.

HCF(9, 2) × LCM(9, 2) = 9 × 2
Since the HCF of 9 and 2 = 1
⇒ 1 × LCM(9, 2) = 18
Therefore, LCM = 18
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