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

HCF of 45 and 180

HCF of 45 and 180 is the largest possible number that divides 45 and 180 exactly without any remainder. The factors of 45 and 180 are 1, 3, 5, 9, 15, 45 and 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 respectively. There are 3 commonly used methods to find the HCF of 45 and 180 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 45 and 180
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 45 and 180?

Answer: HCF of 45 and 180 is 45.

Explanation:

The HCF of two non-zero integers, x(45) and y(180), is the highest positive integer m(45) that divides both x(45) and y(180) without any remainder.

Methods to Find HCF of 45 and 180

Let's look at the different methods for finding the HCF of 45 and 180.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

HCF of 45 and 180 by Long Division

HCF of 45 and 180 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 180 (larger number) by 45 (smaller number).
Step 2: Since the remainder = 0, the divisor (45) is the HCF of 45 and 180.

The corresponding divisor (45) is the HCF of 45 and 180.

HCF of 45 and 180 by Prime Factorization

Prime factorization of 45 and 180 is (3 × 3 × 5) and (2 × 2 × 3 × 3 × 5) respectively. As visible, 45 and 180 have common prime factors. Hence, the HCF of 45 and 180 is 3 × 3 × 5 = 45.

HCF of 45 and 180 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 = 180 and Y = 45

HCF(180, 45) = HCF(45, 180 mod 45) = HCF(45, 0)
HCF(45, 0) = 45 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 45 and 180 is 45.

☛ Also Check:

HCF of 45 and 180 Examples

Example 1: Find the highest number that divides 45 and 180 exactly.

Solution:

The highest number that divides 45 and 180 exactly is their highest common factor, i.e. HCF of 45 and 180.
⇒ Factors of 45 and 180:
- Factors of 45 = 1, 3, 5, 9, 15, 45
- Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
Therefore, the HCF of 45 and 180 is 45.
Example 2: For two numbers, HCF = 45 and LCM = 180. If one number is 45, find the other number.

Solution:

Given: HCF (y, 45) = 45 and LCM (y, 45) = 180
∵ HCF × LCM = 45 × (y)
⇒ y = (HCF × LCM)/45
⇒ y = (45 × 180)/45
⇒ y = 180
Therefore, the other number is 180.
Example 3: The product of two numbers is 8100. If their HCF is 45, what is their LCM?

Solution:

Given: HCF = 45 and product of numbers = 8100
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 8100/45
Therefore, the LCM is 180.

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 45 and 180

What is the HCF of 45 and 180?

The HCF of 45 and 180 is 45. To calculate the HCF of 45 and 180, we need to factor each number (factors of 45 = 1, 3, 5, 9, 15, 45; factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180) and choose the highest factor that exactly divides both 45 and 180, i.e., 45.

If the HCF of 180 and 45 is 45, Find its LCM.

HCF(180, 45) × LCM(180, 45) = 180 × 45
Since the HCF of 180 and 45 = 45
⇒ 45 × LCM(180, 45) = 8100
Therefore, LCM = 180
☛ Highest Common Factor Calculator

How to Find the HCF of 45 and 180 by Long Division Method?

To find the HCF of 45, 180 using long division method, 180 is divided by 45. The corresponding divisor (45) when remainder equals 0 is taken as HCF.

How to Find the HCF of 45 and 180 by Prime Factorization?

To find the HCF of 45 and 180, we will find the prime factorization of the given numbers, i.e. 45 = 3 × 3 × 5; 180 = 2 × 2 × 3 × 3 × 5.
⇒ Since 3, 3, 5 are common terms in the prime factorization of 45 and 180. Hence, HCF(45, 180) = 3 × 3 × 5 = 45
☛ What is a Prime Number?

What are the Methods to Find HCF of 45 and 180?

There are three commonly used methods to find the HCF of 45 and 180.

By Prime Factorization
By Listing Common Factors
By Long Division

What is the Relation Between LCM and HCF of 45, 180?

The following equation can be used to express the relation between LCM and HCF of 45 and 180, i.e. HCF × LCM = 45 × 180.

Download FREE Study Materials

HCF and LCM

Math worksheets and
visual curriculum