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Question

Determine the GCD of 729324 and 32×18 using long division method.


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Solution

First, find the square roots using prime factorization.

729=36
729=36=33=27

324=2×2×3×3×3×3
324=(2×3×3)2=2×9=18

729324=2718=9

32×18
=32×18
=(4×8)×(2×9)
=22×42×32
=2×4×3
=24

GCD of 729324 and 3218 is equivalent to GCD of 9 and 24.

Using long division method,
GCD =3

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