Question

Is 17496 a perfect cube ? If not, find the smallest natural number by which 17496 must be divided so that the quotient is a perfect cube.
please answer my question step by step.
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Answer 1

Answer:

hey there on prime factorization of 17496

you would get 3*3*3*3*3*3*3*2*2*2

here there are 3 triplets of 3 and 2 while one 3

dividing 17496 by 3 you would get the required answer

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ANS---5832

Answer 2

Answer:

Given and Find:

• By what number should 17496 be divided to obtain a perfect cube.

Calculations:

• The number should be divided by the number 3.

⇢ 17,496 ÷ 3

⇢ 5,832

We know that = 17,496 = 3^7 × 2^3

That's,

⇢ 3^7 = (3 × 3 × 3 × 3 × 3 × 3 × 3 = 2187).

⇢ 2^3 = (2 × 2 × 2 = 8).

⇢ 3^7 × 2^3 = (2187 × 8)

⇢ 17,496

⇢ 3 × 3 × 2

⇢ 18