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The product of all the factors of $N = 12^{3} \times 35^{5}$ is

Option 1)
(2⁶ x 3³ x 5⁵ x 7⁵)¹⁰⁰⁸
Option 2)
(2⁶ x 3³ x 5⁵ x 7⁵)¹⁰⁵⁰
Option 3)
(2⁶ x 3³ x 5⁵ x 7⁵)¹⁰⁰⁰
Option 4)
(2⁶ x 3³ x 5⁵ x 7⁵)⁵⁰⁴
Option 5)
(2⁶ x 3³ x 5⁵ x 7⁵)⁵⁰⁸

Answers (1)

R rishi.raj

$12^{2}*35^{5}= 2^{6}*3^{3}*5^{5}*7^{5}$

Total number of factors $= 7*4*6*6=1008$

Multiple of factors $= (2^{6}*3^{3}*5^{5}*7^{5})^{1008/2}$

$(2^{6}*3^{3}*5^{5}*7^{5})^{504}$

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