Question

find the smallest number by which 3645 should be divided so that the quotient is perfect cube

Answer 1

hey!
#ur Ans

first we find prime factors of 3645

3645 = 3×3×3×3×3×3×5

thus, here 5 is not in the pairs so divide by 5, we find the perfect cube umber

3645÷5 = 729

729 is perfect cube number
√729 = 9


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Answer 2

729 = (9)³

LCM of 3645,

3645 = 3 ×3  ×3  × 3  × 3  × 3  ×5

So, the smallest no. by which 3645 should be divided is 5,

3645 ÷ 5 = 3  × 3  ×3  × 3 ×3  ×3 ÷ 5

729 = 3*3*3*3*3*3

729 = (3)³×(3)³

729 = (9)³

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