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HCF of 18 and 45

HCF of 18 and 45 is the largest possible number that divides 18 and 45 exactly without any remainder. The factors of 18 and 45 are 1, 2, 3, 6, 9, 18 and 1, 3, 5, 9, 15, 45 respectively. There are 3 commonly used methods to find the HCF of 18 and 45 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 18 and 45
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 18 and 45?

Answer: HCF of 18 and 45 is 9.

Explanation:

The HCF of two non-zero integers, x(18) and y(45), is the highest positive integer m(9) that divides both x(18) and y(45) without any remainder.

Methods to Find HCF of 18 and 45

The methods to find the HCF of 18 and 45 are explained below.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

HCF of 18 and 45 by Prime Factorization

Prime factorization of 18 and 45 is (2 × 3 × 3) and (3 × 3 × 5) respectively. As visible, 18 and 45 have common prime factors. Hence, the HCF of 18 and 45 is 3 × 3 = 9.

HCF of 18 and 45 by Long Division

HCF of 18 and 45 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 45 (larger number) by 18 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (9).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (9) is the HCF of 18 and 45.

HCF of 18 and 45 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 = 45 and Y = 18

HCF(45, 18) = HCF(18, 45 mod 18) = HCF(18, 9)
HCF(18, 9) = HCF(9, 18 mod 9) = HCF(9, 0)
HCF(9, 0) = 9 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 18 and 45 is 9.

☛ Also Check:

HCF of 18 and 45 Examples

Example 1: Find the HCF of 18 and 45, if their LCM is 90.

Solution:

∵ LCM × HCF = 18 × 45
⇒ HCF(18, 45) = (18 × 45)/90 = 9
Therefore, the highest common factor of 18 and 45 is 9.
Example 2: For two numbers, HCF = 9 and LCM = 90. If one number is 18, find the other number.

Solution:

Given: HCF (x, 18) = 9 and LCM (x, 18) = 90
∵ HCF × LCM = 18 × (x)
⇒ x = (HCF × LCM)/18
⇒ x = (9 × 90)/18
⇒ x = 45
Therefore, the other number is 45.
Example 3: The product of two numbers is 810. If their HCF is 9, what is their LCM?

Solution:

Given: HCF = 9 and product of numbers = 810
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 810/9
Therefore, the LCM is 90.

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FAQs on HCF of 18 and 45

What is the HCF of 18 and 45?

The HCF of 18 and 45 is 9. To calculate the HCF (Highest Common Factor) of 18 and 45, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 45 = 1, 3, 5, 9, 15, 45) and choose the highest factor that exactly divides both 18 and 45, i.e., 9.

How to Find the HCF of 18 and 45 by Long Division Method?

To find the HCF of 18, 45 using long division method, 45 is divided by 18. The corresponding divisor (9) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 18, 45?

The following equation can be used to express the relation between Least Common Multiple and HCF of 18 and 45, i.e. HCF × LCM = 18 × 45.

How to Find the HCF of 18 and 45 by Prime Factorization?

To find the HCF of 18 and 45, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 45 = 3 × 3 × 5.
⇒ Since 3, 3 are common terms in the prime factorization of 18 and 45. Hence, HCF(18, 45) = 3 × 3 = 9
☛ Prime Number

If the HCF of 45 and 18 is 9, Find its LCM.

HCF(45, 18) × LCM(45, 18) = 45 × 18
Since the HCF of 45 and 18 = 9
⇒ 9 × LCM(45, 18) = 810
Therefore, LCM = 90
☛ Highest Common Factor Calculator

What are the Methods to Find HCF of 18 and 45?

There are three commonly used methods to find the HCF of 18 and 45.

By Prime Factorization
By Euclidean Algorithm
By Long Division

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