The smallest natural number, by which 1458 must be divided so that quotient is a perfect cube, is: .

Question

The smallest natural number, by which 1458 must be divided so that quotient is a perfect cube, is: . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

1458 =2 × 36=2 ×(32)3 =2 ×(9)3 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/631b6757fe794dc7b0244868cf303301-.png" /> So to make quotient a perfect cube we have to divide 1458 by 2 Hence, the required number =2.

Q. The smallest natural number, by which 1458 must be divided so that quotient is a perfect cube, is: ________.

$1458 = 2 \times 3^{6} = 2 \times (3^{2})^{3}$
$= 2 \times (9)^{3}$

So to make quotient a perfect cube we have to divide 1458 by 2
Hence, the required number $= 2$ .

Q. The smallest natural number, by which 1458 must be divided so that quotient is a perfect cube, is: ________.

1458=2×36=2×(32)3 =2×(9)3 So to make quotient a perfect cube we have to divide 1458 by 2 Hence, the required number =2.

$1458 = 2 \times 3^{6} = 2 \times (3^{2})^{3}$
$= 2 \times (9)^{3}$

So to make quotient a perfect cube we have to divide 1458 by 2
Hence, the required number $= 2$ .