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HCF of 16 and 21

HCF of 16 and 21 is the largest possible number that divides 16 and 21 exactly without any remainder. The factors of 16 and 21 are 1, 2, 4, 8, 16 and 1, 3, 7, 21 respectively. There are 3 commonly used methods to find the HCF of 16 and 21 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 16 and 21
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 16 and 21?

Answer: HCF of 16 and 21 is 1.

Explanation:

The HCF of two non-zero integers, x(16) and y(21), is the highest positive integer m(1) that divides both x(16) and y(21) without any remainder.

Methods to Find HCF of 16 and 21

The methods to find the HCF of 16 and 21 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

HCF of 16 and 21 by Long Division

HCF of 16 and 21 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 21 (larger number) by 16 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (16) by the remainder (5).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the HCF of 16 and 21.

HCF of 16 and 21 by Prime Factorization

Prime factorization of 16 and 21 is (2 × 2 × 2 × 2) and (3 × 7) respectively. As visible, there are no common prime factors between 16 and 21, i.e. they are coprime. Hence, the HCF of 16 and 21 will be 1.

HCF of 16 and 21 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 21: 1, 3, 7, 21

Since, 1 is the only common factor between 16 and 21. The highest common factor of 16 and 21 is 1.

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HCF of 16 and 21 Examples

Example 1: Find the HCF of 16 and 21, if their LCM is 336.

Solution:

∵ LCM × HCF = 16 × 21
⇒ HCF(16, 21) = (16 × 21)/336 = 1
Therefore, the highest common factor of 16 and 21 is 1.
Example 2: The product of two numbers is 336. If their HCF is 1, what is their LCM?

Solution:

Given: HCF = 1 and product of numbers = 336
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 336/1
Therefore, the LCM is 336.
Example 3: Find the highest number that divides 16 and 21 exactly.

Solution:

The highest number that divides 16 and 21 exactly is their highest common factor, i.e. HCF of 16 and 21.
⇒ Factors of 16 and 21:
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 21 = 1, 3, 7, 21
Therefore, the HCF of 16 and 21 is 1.

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FAQs on HCF of 16 and 21

What is the HCF of 16 and 21?

The HCF of 16 and 21 is 1. To calculate the HCF (Highest Common Factor) of 16 and 21, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 21 = 1, 3, 7, 21) and choose the highest factor that exactly divides both 16 and 21, i.e., 1.

How to Find the HCF of 16 and 21 by Long Division Method?

To find the HCF of 16, 21 using long division method, 21 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, 21?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 16 and 21, i.e. HCF × LCM = 16 × 21.

What are the Methods to Find HCF of 16 and 21?

There are three commonly used methods to find the HCF of 16 and 21.

By Prime Factorization
By Euclidean Algorithm
By Long Division

If the HCF of 21 and 16 is 1, Find its LCM.

HCF(21, 16) × LCM(21, 16) = 21 × 16
Since the HCF of 21 and 16 = 1
⇒ 1 × LCM(21, 16) = 336
Therefore, LCM = 336
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How to Find the HCF of 16 and 21 by Prime Factorization?

To find the HCF of 16 and 21, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 21 = 3 × 7.
⇒ There is no common prime factor for 16 and 21. Hence, HCF (16, 21) = 1.
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