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HCF of 36 and 90

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

1.	HCF of 36 and 90
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 36 and 90?

Answer: HCF of 36 and 90 is 18.

Explanation:

The HCF of two non-zero integers, x(36) and y(90), is the highest positive integer m(18) that divides both x(36) and y(90) without any remainder.

Methods to Find HCF of 36 and 90

Let's look at the different methods for finding the HCF of 36 and 90.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

HCF of 36 and 90 by Long Division

HCF of 36 and 90 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 90 (larger number) by 36 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (36) by the remainder (18).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (18) is the HCF of 36 and 90.

HCF of 36 and 90 by Listing Common Factors

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

There are 6 common factors of 36 and 90, that are 1, 2, 3, 6, 9, and 18. Therefore, the highest common factor of 36 and 90 is 18.

HCF of 36 and 90 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 = 90 and Y = 36

HCF(90, 36) = HCF(36, 90 mod 36) = HCF(36, 18)
HCF(36, 18) = HCF(18, 36 mod 18) = HCF(18, 0)
HCF(18, 0) = 18 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 36 and 90 is 18.

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HCF of 36 and 90 Examples

Example 1: Find the HCF of 36 and 90, if their LCM is 180.

Solution:

∵ LCM × HCF = 36 × 90
⇒ HCF(36, 90) = (36 × 90)/180 = 18
Therefore, the highest common factor of 36 and 90 is 18.
Example 2: Find the highest number that divides 36 and 90 exactly.

Solution:

The highest number that divides 36 and 90 exactly is their highest common factor, i.e. HCF of 36 and 90.
⇒ Factors of 36 and 90:
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Therefore, the HCF of 36 and 90 is 18.
Example 3: The product of two numbers is 3240. If their HCF is 18, what is their LCM?

Solution:

Given: HCF = 18 and product of numbers = 3240
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 3240/18
Therefore, the LCM is 180.

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FAQs on HCF of 36 and 90

What is the HCF of 36 and 90?

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

How to Find the HCF of 36 and 90 by Long Division Method?

To find the HCF of 36, 90 using long division method, 90 is divided by 36. The corresponding divisor (18) when remainder equals 0 is taken as HCF.

If the HCF of 90 and 36 is 18, Find its LCM.

HCF(90, 36) × LCM(90, 36) = 90 × 36
Since the HCF of 90 and 36 = 18
⇒ 18 × LCM(90, 36) = 3240
Therefore, LCM = 180
☛ Highest Common Factor Calculator

How to Find the HCF of 36 and 90 by Prime Factorization?

To find the HCF of 36 and 90, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 90 = 2 × 3 × 3 × 5.
⇒ Since 2, 3, 3 are common terms in the prime factorization of 36 and 90. Hence, HCF(36, 90) = 2 × 3 × 3 = 18
☛ Prime Number

What is the Relation Between LCM and HCF of 36, 90?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 36 and 90, i.e. HCF × LCM = 36 × 90.

What are the Methods to Find HCF of 36 and 90?

There are three commonly used methods to find the HCF of 36 and 90.

By Long Division
By Listing Common Factors
By Prime Factorization

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