Question

Q2. Find the HCF of the following numbers by prime factorisation.
36,72,84
​

Answer 1

Answer:

HCF = 12

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Answer 2

Given:

36, 72, 84

To find:

The HCF of the given numbers using Prime factorization method

Solution:

First,

Prime factorization of 36.

2 | 36

2 | 18

3 | 9

3 | 3

1 | 1

36 = 2² * 3²

Second,

Prime factorization of 72.

2 | 72

2 | 36

2 | 18

3 | 9

3 | 3

1 | 1

72 = 2³ * 3²

Third,

Prime factorization of 84.

2 | 84

2 | 42

3 | 21

7 | 7

1 | 1

84 = 2² * 3¹ * 7¹

At last,

36 = 2² * 3²

72 = 2³ * 3²

84 = 2² * 3¹ * 7¹

To find HCF for Prime factorization

HCF = Product of smallest power of each common Prime factor of numbers.

HCF (36, 72, 84)

= 2² * 3¹

(Here, 2² is the smallest power of common Prime factor and 3¹ is the smallest power of common Prime factor)

= 4 * 3

= 12.

Conclusion:

Therefore, HCF (36, 72, 84) = 12.

Extra Information:

Using Prime factorization we find both HCF and LCM by the following statements,

HCF = Product of smallest power of each common Prime factor of numbers.

LCM = Product of the greatest power of each Prime factor of the numbers.

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