A day full of math games & activities. Find one near you.

HCF of 18 and 20

HCF of 18 and 20 is the largest possible number that divides 18 and 20 exactly without any remainder. The factors of 18 and 20 are 1, 2, 3, 6, 9, 18 and 1, 2, 4, 5, 10, 20 respectively. There are 3 commonly used methods to find the HCF of 18 and 20 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 18 and 20
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 18 and 20?

Answer: HCF of 18 and 20 is 2.

Explanation:

The HCF of two non-zero integers, x(18) and y(20), is the highest positive integer m(2) that divides both x(18) and y(20) without any remainder.

Methods to Find HCF of 18 and 20

Let's look at the different methods for finding the HCF of 18 and 20.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

HCF of 18 and 20 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 = 20 and Y = 18

HCF(20, 18) = HCF(18, 20 mod 18) = HCF(18, 2)
HCF(18, 2) = HCF(2, 18 mod 2) = HCF(2, 0)
HCF(2, 0) = 2 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 18 and 20 is 2.

HCF of 18 and 20 by Long Division

HCF of 18 and 20 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 20 (larger number) by 18 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the HCF of 18 and 20.

HCF of 18 and 20 by Listing Common Factors

Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 20: 1, 2, 4, 5, 10, 20

There are 2 common factors of 18 and 20, that are 1 and 2. Therefore, the highest common factor of 18 and 20 is 2.

☛ Also Check:

HCF of 18 and 20 Examples

Example 1: For two numbers, HCF = 2 and LCM = 180. If one number is 20, find the other number.

Solution:

Given: HCF (y, 20) = 2 and LCM (y, 20) = 180
∵ HCF × LCM = 20 × (y)
⇒ y = (HCF × LCM)/20
⇒ y = (2 × 180)/20
⇒ y = 18
Therefore, the other number is 18.
Example 2: Find the highest number that divides 18 and 20 exactly.

Solution:

The highest number that divides 18 and 20 exactly is their highest common factor, i.e. HCF of 18 and 20.
⇒ Factors of 18 and 20:
- Factors of 18 = 1, 2, 3, 6, 9, 18
- Factors of 20 = 1, 2, 4, 5, 10, 20
Therefore, the HCF of 18 and 20 is 2.
Example 3: Find the HCF of 18 and 20, if their LCM is 180.

Solution:

∵ LCM × HCF = 18 × 20
⇒ HCF(18, 20) = (18 × 20)/180 = 2
Therefore, the highest common factor of 18 and 20 is 2.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on HCF of 18 and 20

What is the HCF of 18 and 20?

The HCF of 18 and 20 is 2. To calculate the HCF of 18 and 20, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 20 = 1, 2, 4, 5, 10, 20) and choose the highest factor that exactly divides both 18 and 20, i.e., 2.

How to Find the HCF of 18 and 20 by Prime Factorization?

To find the HCF of 18 and 20, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 20 = 2 × 2 × 5.
⇒ Since 2 is the only common prime factor of 18 and 20. Hence, HCF (18, 20) = 2.
☛ Prime Number

How to Find the HCF of 18 and 20 by Long Division Method?

To find the HCF of 18, 20 using long division method, 20 is divided by 18. The corresponding divisor (2) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 18 and 20?

There are three commonly used methods to find the HCF of 18 and 20.

By Long Division
By Prime Factorization
By Euclidean Algorithm

What is the Relation Between LCM and HCF of 18, 20?

The following equation can be used to express the relation between LCM and HCF of 18 and 20, i.e. HCF × LCM = 18 × 20.

If the HCF of 20 and 18 is 2, Find its LCM.

HCF(20, 18) × LCM(20, 18) = 20 × 18
Since the HCF of 20 and 18 = 2
⇒ 2 × LCM(20, 18) = 360
Therefore, LCM = 180
☛ HCF Calculator

Download FREE Study Materials

HCF and LCM

Math worksheets and
visual curriculum