HCF of 2 and 9

HCF of 2 and 9 is the largest possible number that divides 2 and 9 exactly without any remainder. The factors of 2 and 9 are 1, 2 and 1, 3, 9 respectively. There are 3 commonly used methods to find the HCF of 2 and 9 - long division, prime factorization, and Euclidean algorithm.

Answer: HCF of 2 and 9 is 1.

Explanation:

The HCF of two non-zero integers, x(2) and y(9), is the highest positive integer m(1) that divides both x(2) and y(9) without any remainder.

Let's look at the different methods for finding the HCF of 2 and 9.

• Using Euclid's Algorithm
• Prime Factorization Method
• Long Division Method

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|, where X ≠ 0)

Therefore, the value of HCF of 2 and 9 is 1.

HCF of 2 and 9 by Prime Factorization

Prime factorization of 2 and 9 is (2) and (3 × 3) respectively. As visible, there are no common prime factors between 2 and 9, i.e. they are co-prime. Hence, the HCF of 2 and 9 will be 1.

HCF of 2 and 9 by Long Division

HCF of 2 and 9 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

• Step 1: Divide 9 (larger number) by 2 (smaller number).
• Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (2) by the remainder (1).
• Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the HCF of 2 and 9.

☛ Also Check:

• HCF of 5, 15 and 20 = 5
• HCF of 60 and 75 = 15
• HCF of 4 and 5 = 1
• HCF of 4052 and 12576 = 4
• HCF of 56 and 88 = 8
• HCF of 396 and 1080 = 36
• HCF of 170 and 238 = 34