HCF of 20 and 21

The HCF of 20 and 21 is 1. The listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 20 and 21. The highest number that divides 20 and 21 perfectly, leaving no remainder, is known as the HCF of 20 and 21. The components of 20 and 21 are, respectively, (1, 2, 4, 5, 10, 20) and (1, 3, 7).

Also read: Highest common factor

What is the HCF of 20 and 21?

The answer to this question is 1. This article shows the HCF of 20 and 21 using various methods for your reference. The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers.

How to Find HCF of 20 and 21?

There are three methods to find the HCF of 20 and 21:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 20 and 21 by Prime Factorisation Method

The prime factorisation of 20 and 21 is given by:

Prime factorisation of 20 = (2 × 2 × 5)

Prime factorisation of 21 = (3 × 7)

Hence, the HCF of 20 and 21 is 1.

HCF (20, 21) = 1

HCF of 20 and 21 by Long Division Method

The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is HCF of 20 and 21.

HCF of 20 and 21

No further division can be done.

Hence, HCF (20, 21) = 1

HCF of 20 and 21 by Listing the Factors

To calculate the HCF of 20 and 21 by listing out the common factors, list the factors as shown below:

Factors of 20 = 1, 2, 4, 5, 10, 20

Factors of 21 = 1, 3, 7, 21

Therefore, the HCF of 20 and 21 is 1.

Related Articles

Video Lesson on Properties of HCF and LCM

HCF of 20 and 21 Solved Example

The product of two numbers is 420. If their HCF is 1, what is their LCM?

Solution:

Given: HCF = 1 and product of numbers = 420

LCM × HCF = product of numbers

⇒ LCM = Product/HCF = 420/1

Therefore, the LCM is 420.

Frequently Asked Questions on HCF of 20 and 21

Q1

What is the HCF of 20 and 21?

The HCF of 20 and 21 is 1. To calculate the Highest common factor of 20 and 21, we need to factor each number and choose the highest factor that exactly divides both 20 and 21, i.e., 1.
Q2

How to Find the HCF of 20 and 21 by Prime Factorisation?

To find the HCF of 20 and 21, we will find the prime factorization of the given numbers, i.e. 20 = 2 × 2 × 5; 21 = 3 × 7.
⇒ There is no common prime factor for 20 and 21. Hence, HCF (20, 21) = 1.
Q3

What are the Methods to Find HCF of 20 and 21?

There are three commonly used methods to find the HCF of 20 and 21.
By Long Division
By Listing Common Factors
By Prime Factorisation
Q4

What is the Relation Between LCM and HCF of 20, 21?

The following equation can be used to express the relation between Least Common Multiple and HCF of 20 and 21, i.e. HCF × LCM = 20 × 21.
Q5

How to Find the HCF of 20 and 21 by Long Division Method?

To find the HCF of 20, 21 using long division method, 21 is divided by 20. The corresponding divisor (1) when remainder equals 0 is taken as HCF.

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