What is HCF of 2 and 10?
HCF of 2 and 10 is the greatest possible number which divides 2 and 10 exactly without any remainder. There are 3 methods commonly used to find the HCF of 2 and 10, i.e. by Long Division, using Factorization, or using the Euclidean Algorithm.
Answer: HCF of 2 and 10 is 2
Explanation:
The HCF (Highest Common Factor) of two or more non-zero integers, X (2) and Y (10), is the largest positive integer M (2), that divides both, X and Y. We can compute the HCF of numbers in many ways, the commonly used methods are listed below.
Methods to Find HCF of 2 and 10
The methods to compute the HCF of 2 and 10 are explained below.
- By Euclidean Algorithm
- By Listing the Common Factors
- By Long Division
HCF of 2 and 10 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 = 10 and Y = 2,
- HCF(10, 2) = HCF(2, 10 mod 2) = HCF(2, 0)
- HCF(2, 0) = 2 (∵ HCF(X, 0) = X)
Therefore, the HCF of 2 and 10 is 2.
HCF of 2 and 10 by Listing the Common Factors
- Factors of 2: 1, 2
- Factors of 10: 1, 2, 5, 10
Common Factors of 2 and 10 are 1, 2. Therefore, the biggest factor which is common to both 2 and 10 here is 2 and this number is the HCF of 2 and 10.
HCF of 2 and 10 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 10 as the dividend and the smaller value 2 as the divisor.
Therefore, the HCF of 2 and 10 = HCF(2, 10) = HCF(10, 2) = 2.
☛ Also Check:
- HCF of 12, 36 - HCF(12, 36) = 12
- HCF of 28, 36 - HCF(28, 36) = 4
- HCF of 196, 38220 - HCF(196, 38220) = 196
- HCF of 391, 425, 527 - HCF(391, 425, 527) = 17
- HCF of 70, 105, 175 - HCF(70, 105, 175) = 35
- HCF of 8, 12 - HCF(8, 12) = 4
- HCF of 3, 5 - HCF(3, 5) = 1