What is HCF of 2 and 9?
HCF of 2 and 9 is the largest possible number that divides 2 and 9 exactly without any remainder. There are 3 methods commonly used to find the HCF of 2 and 9, i.e. by using the Euclidean Algorithm, Long Division, or using Factorization.
Answer: HCF of 2 and 9 is 1
Explanation:
The Highest Common Factor of two or more non-zero integers, X (2) and Y (9), is the largest positive integer M (1), 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 2 and 9
The methods to compute the HCF of 2 and 9 are explained below.
- By Prime Factorization
- By Euclidean Algorithm
- By Long Division
HCF of 2 and 9 by Prime Factorization
HCF is the product of the factors that are common to each of the given numbers.
- Prime Factorization of 2 is 2
- Prime Factorization of 9 is 3 × 3
As visible, there aren't any common prime factors to both 2 and 9, i.e. 2 and 9 are co-prime. This implies that their HCF will be 1 since it is the only common factor.
Hence, the HCF of 9 and 2 is HCF(2, 9) = HCF(9, 2) = 1
HCF of 2 and 9 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 = 9 and Y = 2,
- HCF(9, 2) = HCF(2, 9 mod 2) = HCF(2, 1)
- HCF(2, 1) = HCF(1, 2 mod 1) = HCF(1, 0)
- HCF(1, 0) = 1 (∵ HCF(X, 0) = X)
Therefore, the HCF of 2 and 9 is 1.
HCF of 2 and 9 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 number.
- 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 9 as the dividend and the smaller value 2 as the divisor.
Therefore, the HCF of 2 and 9 = HCF(2, 9) = HCF(9, 2) = 1.
☛ Also Check:
- HCF of 4, 6 - HCF(4, 6) = 2
- HCF of 12, 15, 18 - HCF(12, 15, 18) = 3
- HCF of 20, 28, 36 - HCF(20, 28, 36) = 4
- HCF of 144, 180 - HCF(144, 180) = 36
- HCF of 8, 20 - HCF(8, 20) = 4
- HCF of 4052, 12576 - HCF(4052, 12576) = 4
- HCF of 64, 96 - HCF(64, 96) = 32