Question

Divide the number 26244 by the smallest number so that the quotient is perfect cube so the smallest number from the option A)4 B) 6 C)36 D)16

Answer 1

Answer:

Option C - 36

Step-by-step explanation:

Given : Number 26244

To find : Divide the number by the smallest number so that the quotient is perfect cube so the smallest number ?

Solution :

Factor the number 26244.

$26244=2\times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times3$

$26244=2^2\times 3^3\times 3^3\times 3^2$

$26244=(3\times 3)^3\times 2^2\times3^2$

$26244=(3\times 3)^3\times 36$

To make it a perfect cube we divide the number by 36.

$\frac{26244}{36}=\frac{(3\times 3)^3\times 36}{36}$

$729=9^3$

Therefore, Option C is correct.