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HCF of 15 and 18

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

1.	HCF of 15 and 18
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 15 and 18?

Answer: HCF of 15 and 18 is 3.

Explanation:

The HCF of two non-zero integers, x(15) and y(18), is the highest positive integer m(3) that divides both x(15) and y(18) without any remainder.

Methods to Find HCF of 15 and 18

The methods to find the HCF of 15 and 18 are explained below.

Long Division Method
Using Euclid's Algorithm
Prime Factorization Method

HCF of 15 and 18 by Long Division

HCF of 15 and 18 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 18 (larger number) by 15 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (15) by the remainder (3).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the HCF of 15 and 18.

HCF of 15 and 18 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 = 18 and Y = 15

HCF(18, 15) = HCF(15, 18 mod 15) = HCF(15, 3)
HCF(15, 3) = HCF(3, 15 mod 3) = HCF(3, 0)
HCF(3, 0) = 3 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 15 and 18 is 3.

HCF of 15 and 18 by Prime Factorization

Prime factorization of 15 and 18 is (3 × 5) and (2 × 3 × 3) respectively. As visible, 15 and 18 have only one common prime factor i.e. 3. Hence, the HCF of 15 and 18 is 3.

☛ Also Check:

HCF of 15 and 18 Examples

Example 1: Find the HCF of 15 and 18, if their LCM is 90.

Solution:

∵ LCM × HCF = 15 × 18
⇒ HCF(15, 18) = (15 × 18)/90 = 3
Therefore, the highest common factor of 15 and 18 is 3.
Example 2: Find the highest number that divides 15 and 18 exactly.

Solution:

The highest number that divides 15 and 18 exactly is their highest common factor, i.e. HCF of 15 and 18.
⇒ Factors of 15 and 18:
- Factors of 15 = 1, 3, 5, 15
- Factors of 18 = 1, 2, 3, 6, 9, 18
Therefore, the HCF of 15 and 18 is 3.
Example 3: The product of two numbers is 270. If their HCF is 3, what is their LCM?

Solution:

Given: HCF = 3 and product of numbers = 270
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 270/3
Therefore, the LCM is 90.

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FAQs on HCF of 15 and 18

What is the HCF of 15 and 18?

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

How to Find the HCF of 15 and 18 by Prime Factorization?

To find the HCF of 15 and 18, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 18 = 2 × 3 × 3.
⇒ Since 3 is the only common prime factor of 15 and 18. Hence, HCF (15, 18) = 3.
☛ What is a Prime Number?

What are the Methods to Find HCF of 15 and 18?

There are three commonly used methods to find the HCF of 15 and 18.

By Long Division
By Prime Factorization
By Euclidean Algorithm

How to Find the HCF of 15 and 18 by Long Division Method?

To find the HCF of 15, 18 using long division method, 18 is divided by 15. The corresponding divisor (3) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 15, 18?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 15 and 18, i.e. HCF × LCM = 15 × 18.

If the HCF of 18 and 15 is 3, Find its LCM.

HCF(18, 15) × LCM(18, 15) = 18 × 15
Since the HCF of 18 and 15 = 3
⇒ 3 × LCM(18, 15) = 270
Therefore, LCM = 90
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