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HCF of 15 and 27

HCF of 15 and 27 is the largest possible number that divides 15 and 27 exactly without any remainder. The factors of 15 and 27 are 1, 3, 5, 15 and 1, 3, 9, 27 respectively. There are 3 commonly used methods to find the HCF of 15 and 27 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 15 and 27
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 15 and 27?

Answer: HCF of 15 and 27 is 3.

Explanation:

The HCF of two non-zero integers, x(15) and y(27), is the highest positive integer m(3) that divides both x(15) and y(27) without any remainder.

Methods to Find HCF of 15 and 27

Let's look at the different methods for finding the HCF of 15 and 27.

Listing Common Factors
Long Division Method
Using Euclid's Algorithm

HCF of 15 and 27 by Listing Common Factors

Factors of 15: 1, 3, 5, 15
Factors of 27: 1, 3, 9, 27

There are 2 common factors of 15 and 27, that are 1 and 3. Therefore, the highest common factor of 15 and 27 is 3.

HCF of 15 and 27 by Long Division

HCF of 15 and 27 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 27 (larger number) by 15 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (15) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the HCF of 15 and 27.

HCF of 15 and 27 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 = 27 and Y = 15

HCF(27, 15) = HCF(15, 27 mod 15) = HCF(15, 12)
HCF(15, 12) = HCF(12, 15 mod 12) = HCF(12, 3)
HCF(12, 3) = HCF(3, 12 mod 3) = HCF(3, 0)
HCF(3, 0) = 3 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 15 and 27 is 3.

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HCF of 15 and 27 Examples

Example 1: Find the highest number that divides 15 and 27 exactly.

Solution:

The highest number that divides 15 and 27 exactly is their highest common factor, i.e. HCF of 15 and 27.
⇒ Factors of 15 and 27:
- Factors of 15 = 1, 3, 5, 15
- Factors of 27 = 1, 3, 9, 27
Therefore, the HCF of 15 and 27 is 3.
Example 2: Find the HCF of 15 and 27, if their LCM is 135.

Solution:

∵ LCM × HCF = 15 × 27
⇒ HCF(15, 27) = (15 × 27)/135 = 3
Therefore, the highest common factor of 15 and 27 is 3.
Example 3: The product of two numbers is 405. If their HCF is 3, what is their LCM?

Solution:

Given: HCF = 3 and product of numbers = 405
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 405/3
Therefore, the LCM is 135.

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FAQs on HCF of 15 and 27

What is the HCF of 15 and 27?

The HCF of 15 and 27 is 3. To calculate the HCF (Highest Common Factor) of 15 and 27, we need to factor each number (factors of 15 = 1, 3, 5, 15; factors of 27 = 1, 3, 9, 27) and choose the highest factor that exactly divides both 15 and 27, i.e., 3.

If the HCF of 27 and 15 is 3, Find its LCM.

HCF(27, 15) × LCM(27, 15) = 27 × 15
Since the HCF of 27 and 15 = 3
⇒ 3 × LCM(27, 15) = 405
Therefore, LCM = 135
☛ Highest Common Factor Calculator

How to Find the HCF of 15 and 27 by Prime Factorization?

To find the HCF of 15 and 27, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 27 = 3 × 3 × 3.
⇒ Since 3 is the only common prime factor of 15 and 27. Hence, HCF (15, 27) = 3.
☛ Prime Number

What is the Relation Between LCM and HCF of 15, 27?

The following equation can be used to express the relation between LCM and HCF of 15 and 27, i.e. HCF × LCM = 15 × 27.

What are the Methods to Find HCF of 15 and 27?

There are three commonly used methods to find the HCF of 15 and 27.

By Listing Common Factors
By Long Division
By Prime Factorization

How to Find the HCF of 15 and 27 by Long Division Method?

To find the HCF of 15, 27 using long division method, 27 is divided by 15. The corresponding divisor (3) when remainder equals 0 is taken as HCF.

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