Question

find the HCF of 96,528,1584,2016​

Answer 1

Let us find out the HCF of 96, 528, 1584, 2016 through prime factorisation method.

✴ Prime factors of 96 = 2 × 2 × 2 × 2 × 2 × 3

✴ Prime factors of 528 = 2 × 2 × 2 × 2 × 3 × 11

✴ Prime factorisation of 1584 = 2 × 2 × 2 × 2 × 3 × 3 × 11

✴ Prime factorisation of 2016 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 7

➡ Common Factors of 96, 528, 1584, 2016 = 2 × 2 × 2 × 2 × 3 = 48

Thus, HCF of 96, 528, 1584, 2016 is 48.

Answer 2

$96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3$

$528 = 2 \times 2 \times 2 \times 2 \times 3 \times 11$

$1584 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 11$

$2016 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times \times 7$

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$96 = {2}^{5} \times {3}^{1}$

$528 = {2}^{4} \times {3}^{1} \times {11}^{1}$

$1584 = {2}^{4} \times {3}^{2} \times {11}^{1}$

$2016 = {2}^{5} \times {3}^{2} \times {7}^{1}$

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So HCF=

${2}^{4} \times {3}^{1}$

$2 \times 2 \times 2 \times 2 \times 3$

$= 48$