HCF of 20 and 21 is the largest possible number that divides 20 and 21 exactly without any remainder. The factors of 20 and 21 are 1, 2, 4, 5, 10, 20 and 1, 3, 7, 21 respectively. There are 3 commonly used methods to find the HCF of 20 and 21 - long division, Euclidean algorithm, and prime factorization.
| 1. | HCF of 20 and 21 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is HCF of 20 and 21?
Answer: HCF of 20 and 21 is 1.
Explanation:
The HCF of two non-zero integers, x(20) and y(21), is the highest positive integer m(1) that divides both x(20) and y(21) without any remainder.
Methods to Find HCF of 20 and 21
Let's look at the different methods for finding the HCF of 20 and 21.
- Prime Factorization Method
- Long Division Method
- Using Euclid's Algorithm
HCF of 20 and 21 by Prime Factorization
Prime factorization of 20 and 21 is (2 × 2 × 5) and (3 × 7) respectively. As visible, there are no common prime factors between 20 and 21, i.e. they are co-prime. Hence, the HCF of 20 and 21 will be 1.
HCF of 20 and 21 by Long Division
HCF of 20 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 20 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (20) by the remainder (1).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (1) is the HCF of 20 and 21.
HCF of 20 and 21 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 = 21 and Y = 20
- HCF(21, 20) = HCF(20, 21 mod 20) = HCF(20, 1)
- HCF(20, 1) = HCF(1, 20 mod 1) = HCF(1, 0)
- HCF(1, 0) = 1 (∵ HCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of HCF of 20 and 21 is 1.
☛ Also Check:
- HCF of 18 and 27 = 9
- HCF of 20 and 35 = 5
- HCF of 4 and 6 = 2
- HCF of 17, 23 and 29 = 1
- HCF of 72 and 120 = 24
- HCF of 18, 54 and 81 = 9
- HCF of 455 and 42 = 7
HCF of 20 and 21 Examples
Example 1: 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.Example 2: Find the HCF of 20 and 21, if their LCM is 420.
Solution:
∵ LCM × HCF = 20 × 21
⇒ HCF(20, 21) = (20 × 21)/420 = 1
Therefore, the highest common factor of 20 and 21 is 1.Example 3: Find the highest number that divides 20 and 21 exactly.
Solution:
The highest number that divides 20 and 21 exactly is their highest common factor, i.e. HCF of 20 and 21.
⇒ Factors of 20 and 21:- 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.
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FAQs on HCF of 20 and 21
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 (factors of 20 = 1, 2, 4, 5, 10, 20; factors of 21 = 1, 3, 7, 21) and choose the highest factor that exactly divides both 20 and 21, i.e., 1.
How to Find the HCF of 20 and 21 by Prime Factorization?
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.
☛ What are Prime Numbers?
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.
If the HCF of 21 and 20 is 1, Find its LCM.
HCF(21, 20) × LCM(21, 20) = 21 × 20
Since the HCF of 21 and 20 = 1
⇒ 1 × LCM(21, 20) = 420
Therefore, LCM = 420
☛ Highest Common Factor Calculator
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 Listing Common Factors
- By Long Division
- By Prime Factorization
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.
