What is HCF of 9 and 21?
HCF of 9 and 21 is the highest possible number that divides 9 and 21 exactly without any remainder. There are 3 methods commonly used to find the HCF of 9 and 21, i.e. by Factorization, using the Euclidean Algorithm, or using Long Division.
Answer: HCF of 9 and 21 is 3
Explanation:
The Highest Common Factor (HCF) of two or more non-zero integers, X (9) and Y (21), is the largest positive integer M (3), that divides both, X and Y. We can calculate the HCF of numbers in many ways, the commonly used methods are listed below.
Methods to Find HCF of 9 and 21
The methods to compute the HCF of 9 and 21 are explained below.
- By Prime Factorization
- By Euclid's Algorithm
- By Long Division
HCF of 9 and 21 by Prime Factorization
HCF is the product of the factors that are common to each of the given numbers.
- Prime Factorization of 9 is 3 × 3
- Prime Factorization of 21 is 3 × 7
As visible, 9 and 21 have common prime factors. Here 3 is the only common factor.
Hence, the HCF of 21 and 9 is HCF(9, 21) = HCF(21, 9) = 3
HCF of 9 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 = 9,
- HCF(21, 9) = HCF(9, 21 mod 9) = HCF(9, 3)
- HCF(9, 3) = HCF(3, 9 mod 3) = HCF(3, 0)
- HCF(3, 0) = 3 (∵ HCF(X, 0) = X)
Therefore, the HCF of 9 and 21 is 3.
HCF of 9 and 21 by Long Division
HCF is the product of the factors that are common to each of the given numbers.
- Step 1: Divide the larger number by the smaller one.
- Step 2: Divide the dividend by the remainder obtained in Step 1 and repeat this step until we get the remainder as 0.
- Step 3: The last dividend is the HCF of the two numbers.
Here, we take the larger value 21 as the dividend and the smaller value 9 as the divisor.
Therefore, the HCF of 9 and 21 = HCF(9, 21) = HCF(21, 9) = 3.
☛ Also Check:
- HCF of 27, 45 - HCF(27, 45) = 9
- HCF of 12, 20 - HCF(12, 20) = 4
- HCF of 8, 16 - HCF(8, 16) = 8
- HCF of 24, 36, 40 - HCF(24, 36, 40) = 4
- HCF of 144, 198 - HCF(144, 198) = 18
- HCF of 84, 90 - HCF(84, 90) = 6
- HCF of 12, 30 - HCF(12, 30) = 6