Question

find the HCF of 12 16 and 28
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Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

Methods to Find HCF of 12, 16 and 28

The methods to find the HCF of 12, 16 and 28 are explained below.

Long Division Method

Prime Factorization Method

Using Euclid's Algorithm

HCF of 12, 16 and 28 by Long Division

HCF of 12, 16 and 28 by Long Division

HCF of 12, 16 and 28 can be represented as HCF of (HCF of 12, 16) and 28. HCF(12, 16, 28) can be thus calculated by first finding HCF(12, 16) using long division and thereafter using this result with 28 to perform long division again.

Step 1: Divide 16 (larger number) by 12 (smaller number).

Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (4). Repeat this process until the remainder = 0.

⇒ HCF(12, 16) = 4.

Step 3: Now to find the HCF of 4 and 28, we will perform a long division on 28 and 4.

Step 4: For remainder = 0, divisor = 4 ⇒ HCF(4, 28) = 4

Thus, HCF(12, 16, 28) = HCF(HCF(12, 16), 28) = 4.

HCF of 12, 16 and 28 by Prime Factorization

Prime factorization of 12, 16 and 28 is (2 × 2 × 3), (2 × 2 × 2 × 2) and (2 × 2 × 7) respectively. As visible, 12, 16 and 28 have common prime factors. Hence, the HCF of 12, 16 and 28 is 2 × 2 = 4.

HCF of 12, 16 and 28 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, 28) = HCF(HCF(12, 16), 28)

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, 28)

HCF(28, 4) = HCF(4, 28 mod 4) = HCF(4, 0)

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

Therefore, the value of HCF of 12, 16 and 28 is 4.