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HCF of 27 and 36

HCF of 27 and 36 is the largest possible number that divides 27 and 36 exactly without any remainder. The factors of 27 and 36 are 1, 3, 9, 27 and 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively. There are 3 commonly used methods to find the HCF of 27 and 36 - long division, prime factorization, and Euclidean algorithm.

1.	HCF of 27 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 27 and 36?

Answer: HCF of 27 and 36 is 9.

Explanation:

The HCF of two non-zero integers, x(27) and y(36), is the highest positive integer m(9) that divides both x(27) and y(36) without any remainder.

Methods to Find HCF of 27 and 36

The methods to find the HCF of 27 and 36 are explained below.

Long Division Method
Using Euclid's Algorithm
Prime Factorization Method

HCF of 27 and 36 by Long Division

HCF of 27 and 36 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 36 (larger number) by 27 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (27) by the remainder (9).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (9) is the HCF of 27 and 36.

HCF of 27 and 36 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 = 36 and Y = 27

HCF(36, 27) = HCF(27, 36 mod 27) = HCF(27, 9)
HCF(27, 9) = HCF(9, 27 mod 9) = HCF(9, 0)
HCF(9, 0) = 9 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 27 and 36 is 9.

HCF of 27 and 36 by Prime Factorization

Prime factorization of 27 and 36 is (3 × 3 × 3) and (2 × 2 × 3 × 3) respectively. As visible, 27 and 36 have common prime factors. Hence, the HCF of 27 and 36 is 3 × 3 = 9.

☛ Also Check:

HCF of 27 and 36 Examples

Example 1: Find the highest number that divides 27 and 36 exactly.

Solution:

The highest number that divides 27 and 36 exactly is their highest common factor, i.e. HCF of 27 and 36.
⇒ Factors of 27 and 36:
- Factors of 27 = 1, 3, 9, 27
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Therefore, the HCF of 27 and 36 is 9.
Example 2: The product of two numbers is 972. If their HCF is 9, what is their LCM?

Solution:

Given: HCF = 9 and product of numbers = 972
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 972/9
Therefore, the LCM is 108.
Example 3: Find the HCF of 27 and 36, if their LCM is 108.

Solution:

∵ LCM × HCF = 27 × 36
⇒ HCF(27, 36) = (27 × 36)/108 = 9
Therefore, the highest common factor of 27 and 36 is 9.

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FAQs on HCF of 27 and 36

What is the HCF of 27 and 36?

The HCF of 27 and 36 is 9. To calculate the Highest common factor (HCF) of 27 and 36, we need to factor each number (factors of 27 = 1, 3, 9, 27; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the highest factor that exactly divides both 27 and 36, i.e., 9.

How to Find the HCF of 27 and 36 by Long Division Method?

To find the HCF of 27, 36 using long division method, 36 is divided by 27. The corresponding divisor (9) when remainder equals 0 is taken as HCF.

How to Find the HCF of 27 and 36 by Prime Factorization?

To find the HCF of 27 and 36, we will find the prime factorization of the given numbers, i.e. 27 = 3 × 3 × 3; 36 = 2 × 2 × 3 × 3.
⇒ Since 3, 3 are common terms in the prime factorization of 27 and 36. Hence, HCF(27, 36) = 3 × 3 = 9
☛ What are Prime Numbers?

If the HCF of 36 and 27 is 9, Find its LCM.

HCF(36, 27) × LCM(36, 27) = 36 × 27
Since the HCF of 36 and 27 = 9
⇒ 9 × LCM(36, 27) = 972
Therefore, LCM = 108
☛ Highest Common Factor Calculator

What are the Methods to Find HCF of 27 and 36?

There are three commonly used methods to find the HCF of 27 and 36.

By Prime Factorization
By Long Division
By Listing Common Factors

What is the Relation Between LCM and HCF of 27, 36?

The following equation can be used to express the relation between Least Common Multiple and HCF of 27 and 36, i.e. HCF × LCM = 27 × 36.

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