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HCF of 16 and 27

HCF of 16 and 27 is the largest possible number that divides 16 and 27 exactly without any remainder. The factors of 16 and 27 are 1, 2, 4, 8, 16 and 1, 3, 9, 27 respectively. There are 3 commonly used methods to find the HCF of 16 and 27 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 16 and 27
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 16 and 27?

Answer: HCF of 16 and 27 is 1.

Explanation:

The HCF of two non-zero integers, x(16) and y(27), is the highest positive integer m(1) that divides both x(16) and y(27) without any remainder.

Methods to Find HCF of 16 and 27

Let's look at the different methods for finding the HCF of 16 and 27.

Listing Common Factors
Long Division Method
Prime Factorization Method

HCF of 16 and 27 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 27: 1, 3, 9, 27

Since, 1 is the only common factor between 16 and 27. The highest common factor of 16 and 27 is 1.

HCF of 16 and 27 by Long Division

HCF of 16 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 16 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (16) by the remainder (11).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the HCF of 16 and 27.

HCF of 16 and 27 by Prime Factorization

Prime factorization of 16 and 27 is (2 × 2 × 2 × 2) and (3 × 3 × 3) respectively. As visible, there are no common prime factors between 16 and 27, i.e. they are coprime. Hence, the HCF of 16 and 27 will be 1.

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HCF of 16 and 27 Examples

Example 1: The product of two numbers is 432. If their HCF is 1, what is their LCM?

Solution:

Given: HCF = 1 and product of numbers = 432
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 432/1
Therefore, the LCM is 432.
Example 2: For two numbers, HCF = 1 and LCM = 432. If one number is 27, find the other number.

Solution:

Given: HCF (z, 27) = 1 and LCM (z, 27) = 432
∵ HCF × LCM = 27 × (z)
⇒ z = (HCF × LCM)/27
⇒ z = (1 × 432)/27
⇒ z = 16
Therefore, the other number is 16.
Example 3: Find the highest number that divides 16 and 27 exactly.

Solution:

The highest number that divides 16 and 27 exactly is their highest common factor, i.e. HCF of 16 and 27.
⇒ Factors of 16 and 27:
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 27 = 1, 3, 9, 27
Therefore, the HCF of 16 and 27 is 1.

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FAQs on HCF of 16 and 27

What is the HCF of 16 and 27?

The HCF of 16 and 27 is 1. To calculate the HCF (Highest Common Factor) of 16 and 27, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 27 = 1, 3, 9, 27) and choose the highest factor that exactly divides both 16 and 27, i.e., 1.

How to Find the HCF of 16 and 27 by Prime Factorization?

To find the HCF of 16 and 27, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 27 = 3 × 3 × 3.
⇒ There is no common prime factor for 16 and 27. Hence, HCF (16, 27) = 1.
☛ Prime Number

What are the Methods to Find HCF of 16 and 27?

There are three commonly used methods to find the HCF of 16 and 27.

By Listing Common Factors
By Prime Factorization
By Long Division

If the HCF of 27 and 16 is 1, Find its LCM.

HCF(27, 16) × LCM(27, 16) = 27 × 16
Since the HCF of 27 and 16 = 1
⇒ 1 × LCM(27, 16) = 432
Therefore, LCM = 432
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How to Find the HCF of 16 and 27 by Long Division Method?

To find the HCF of 16, 27 using long division method, 27 is divided by 16. The corresponding divisor (1) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 16, 27?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 16 and 27, i.e. HCF × LCM = 16 × 27.

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