Question

using division method find hcf of 12 , 16 and 32

Answer 1

Answer:

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Step-by-step explanation:

HCF of 12, 16 and 18 is the largest possible number that divides 12, 16 and 18 exactly without any remainder. The factors of 12, 16 and 18 are (1, 2, 3, 4, 6, 12), (1, 2, 4, 8, 16) and (1, 2, 3, 6, 9, 18) respectively. There are 3 commonly used methods to find the HCF of 12, 16 and 18 - prime factorization, long division, and Euclidean algorithmWhat is HCF of 12, 16 and 18?

Answer: HCF of 12, 16 and 18 is 2.

HCF of 12, 16 and 18

Explanation:

The HCF of three non-zero integers, x(12), y(16) and z(18), is the highest positive integer m(2) that divides x(12), y(16) and z(18) without any remainder.Methods to Find HCF of 12, 16 and 18

The methods to find the HCF of 12, 16 and 18 are explained below.

Listing Common Factors

Prime Factorization Method

Using Euclid's Algorithm

HCF of 12, 16 and 18 by Listing Common Factors

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 16: 1, 2, 4, 8, 16

Factors of 18: 1, 2, 3, 6, 9, 18

There are 2 common factors of 12, 16 and 18, that are 1 and 2. Therefore, the highest common factor of 12, 16 and 18 is 2.HCF of 12, 16 and 18 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.

HCF(12, 16, 18) = HCF(HCF(12, 16), 18)

HCF(16, 12) = HCF(12, 16 mod 12) = HCF(12, 4)

HCF(12, 4) = HCF(4, 12 mod 4) = HCF(4, 0)

HCF(4, 0) = 4 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Steps for HCF(4, 18)

HCF(18, 4) = HCF(4, 18 mod 4) = HCF(4, 2)

HCF(4, 2) = HCF(2, 4 mod 2) = HCF(2, 0)

HCF(2, 0) = 2 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 12, 16 and 18 is 2.

Answer 2

Answer:

12)16(1

- 12

04)12(3

- 12

00

4 )32(8

- 32

00

The Ans is-4