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HCF of 27 and 63

HCF of 27 and 63 is the largest possible number that divides 27 and 63 exactly without any remainder. The factors of 27 and 63 are 1, 3, 9, 27 and 1, 3, 7, 9, 21, 63 respectively. There are 3 commonly used methods to find the HCF of 27 and 63 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 27 and 63
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 27 and 63?

Answer: HCF of 27 and 63 is 9.

Explanation:

The HCF of two non-zero integers, x(27) and y(63), is the highest positive integer m(9) that divides both x(27) and y(63) without any remainder.

Methods to Find HCF of 27 and 63

Let's look at the different methods for finding the HCF of 27 and 63.

Listing Common Factors
Prime Factorization Method
Using Euclid's Algorithm

HCF of 27 and 63 by Listing Common Factors

Factors of 27: 1, 3, 9, 27
Factors of 63: 1, 3, 7, 9, 21, 63

There are 3 common factors of 27 and 63, that are 1, 3, and 9. Therefore, the highest common factor of 27 and 63 is 9.

HCF of 27 and 63 by Prime Factorization

Prime factorization of 27 and 63 is (3 × 3 × 3) and (3 × 3 × 7) respectively. As visible, 27 and 63 have common prime factors. Hence, the HCF of 27 and 63 is 3 × 3 = 9.

HCF of 27 and 63 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 = 63 and Y = 27

HCF(63, 27) = HCF(27, 63 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 63 is 9.

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HCF of 27 and 63 Examples

Example 1: Find the HCF of 27 and 63, if their LCM is 189.

Solution:

∵ LCM × HCF = 27 × 63
⇒ HCF(27, 63) = (27 × 63)/189 = 9
Therefore, the highest common factor of 27 and 63 is 9.
Example 2: The product of two numbers is 1701. If their HCF is 9, what is their LCM?

Solution:

Given: HCF = 9 and product of numbers = 1701
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 1701/9
Therefore, the LCM is 189.
Example 3: For two numbers, HCF = 9 and LCM = 189. If one number is 27, find the other number.

Solution:

Given: HCF (x, 27) = 9 and LCM (x, 27) = 189
∵ HCF × LCM = 27 × (x)
⇒ x = (HCF × LCM)/27
⇒ x = (9 × 189)/27
⇒ x = 63
Therefore, the other number is 63.

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FAQs on HCF of 27 and 63

What is the HCF of 27 and 63?

The HCF of 27 and 63 is 9. To calculate the Highest common factor (HCF) of 27 and 63, we need to factor each number (factors of 27 = 1, 3, 9, 27; factors of 63 = 1, 3, 7, 9, 21, 63) and choose the highest factor that exactly divides both 27 and 63, i.e., 9.

If the HCF of 63 and 27 is 9, Find its LCM.

HCF(63, 27) × LCM(63, 27) = 63 × 27
Since the HCF of 63 and 27 = 9
⇒ 9 × LCM(63, 27) = 1701
Therefore, LCM = 189
☛ Highest Common Factor Calculator

What are the Methods to Find HCF of 27 and 63?

There are three commonly used methods to find the HCF of 27 and 63.

By Prime Factorization
By Listing Common Factors
By Long Division

How to Find the HCF of 27 and 63 by Long Division Method?

To find the HCF of 27, 63 using long division method, 63 is divided by 27. The corresponding divisor (9) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 27, 63?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 27 and 63, i.e. HCF × LCM = 27 × 63.

How to Find the HCF of 27 and 63 by Prime Factorization?

To find the HCF of 27 and 63, we will find the prime factorization of the given numbers, i.e. 27 = 3 × 3 × 3; 63 = 3 × 3 × 7.
⇒ Since 3, 3 are common terms in the prime factorization of 27 and 63. Hence, HCF(27, 63) = 3 × 3 = 9
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