What is HCF of 9 and 11?
HCF of 9 and 11 is the highest possible number which divides 9 and 11 exactly without any remainder. There are 3 methods commonly used to find the HCF of 9 and 11, i.e. by Factorization, using Long Division, or using the Euclidean Algorithm.
Answer: HCF of 9 and 11 is 1
Explanation:
The Highest Common Factor of two or more non-zero integers, X (9) and Y (11), is the largest positive integer M (1), that divides both, X and Y. We can find the HCF of numbers in many ways, the commonly used methods are listed below.
Methods to Find HCF of 9 and 11
The methods to compute the HCF of 9 and 11 are explained below.
- By Euclid's Algorithm
- By Listing the Common Factors
- By Long Division
HCF of 9 and 11 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 = 11 and Y = 9,
- HCF(11, 9) = HCF(9, 11 mod 9) = HCF(9, 2)
- HCF(9, 2) = HCF(2, 9 mod 2) = HCF(2, 1)
- HCF(2, 1) = 1 (∵ HCF(X, 1) = 1)
Therefore, the HCF of 9 and 11 is 1.
HCF of 9 and 11 by Listing the Common Factors
- Factors of 9: 1, 3, 9
- Factors of 11: 1, 11
There is only one common factor between 9 and 11 i.e. 1. Hence, 1 is the HCF of 9 and 11. This also implies that the 9 and 11 are coprime.
HCF of 9 and 11 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 11 as the dividend and the smaller value 9 as the divisor.
Therefore, the HCF of 9 and 11 = HCF(9, 11) = HCF(11, 9) = 1.
☛ Also Check:
- HCF of 4052, 420 - HCF(4052, 420) = 4
- HCF of 64, 96 - HCF(64, 96) = 32
- HCF of 4, 6 - HCF(4, 6) = 2
- HCF of 18, 27 - HCF(18, 27) = 9
- HCF of 4052, 12576 - HCF(4052, 12576) = 4
- HCF of 12, 18, 24 - HCF(12, 18, 24) = 6
- HCF of 45, 30 - HCF(45, 30) = 15