What is HCF of 21 and 29?
HCF of 21 and 29 is the highest possible number that divides 21 and 29 exactly without any remainder. There are 3 methods commonly used to find the HCF of 21 and 29, i.e. by using the Euclidean Algorithm, Long Division, or using Factorization.
Answer: HCF of 21 and 29 is 1
Explanation:
The HCF of two or more non-zero integers, X (21) and Y (29), 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 21 and 29
The methods to compute the HCF of 21 and 29 are explained below.
- By Listing the Common Factors
- By Long Division
- By Euclidean Algorithm
HCF of 21 and 29 by Listing the Common Factors
- Factors of 21: 1, 3, 7, 21
- Factors of 29: 1, 29
There is only one common factor between 21 and 29 i.e. 1. Therefore, 1 is the HCF of 21 and 29. This also implies that the 21 and 29 are co-prime.
HCF of 21 and 29 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 29 as the dividend and the smaller value 21 as the divisor.
HCF of 21 and 29 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 = 29 and Y = 21,
- HCF(29, 21) = HCF(21, 29 mod 21) = HCF(21, 8)
- HCF(21, 8) = HCF(8, 21 mod 8) = HCF(8, 5)
- HCF(8, 5) = HCF(5, 8 mod 5) = HCF(5, 3)
- HCF(5, 3) = HCF(3, 5 mod 3) = HCF(3, 2)
- HCF(3, 2) = HCF(2, 3 mod 2) = HCF(2, 1)
- HCF(2, 1) = 1 (∵ HCF(X, 1) = 1)
Therefore, the HCF of 21 and 29 is 1.
Therefore, the HCF of 21 and 29 = HCF(21, 29) = HCF(29, 21) = 1.
☛ Also Check:
- HCF of 12, 16, 18 - HCF(12, 16, 18) = 2
- HCF of 91, 112, 49 - HCF(91, 112, 49) = 7
- HCF of 27, 63 - HCF(27, 63) = 9
- HCF of 8, 12 - HCF(8, 12) = 4
- HCF of 14, 21 - HCF(14, 21) = 7
- HCF of 5, 10 - HCF(5, 10) = 5
- HCF of 144, 180 - HCF(144, 180) = 36