Question

Divide the number 13122 by the smallest number so that the quotient is a perfect cube

Answer 1

any number, X= divisor× quotient ( if the divisor perfectly divides the number X )

13122= 2×3×3×3×3×3×3×3×3
= 2×3×(3×3)×(3×3)×(3×3)
= 6 × 9×9×9
(9×9×9)=729 is a perfect cube
therefore the smallest number to divide 13122 so that the quotient a perfect cube = 6
and the perfect cube =729

Answer 2

Given : The main number is 13122

To find : The smallest number by which the number 13122 should be divided to get a perfect cube as the quotient.

Solution :

The required smallest number is 18

We can simply solve this mathematical problem by using the following mathematical process.

First of all, we have to factorise the main number into its prime factors.

So,

13122 = 2×3×3×3×3×3×3×3×3

Now, we have to group the factors in triples of equal factors.

So,

13122 = 2×3×3×(3×3×3)×(3×3×3)

Now, product of the leftover factors which are outside the triples of equal factors, will be the required smallest number.

Leftover factors = 2,3,3

Required smallest number = 2×3×3 = 18

Verification :

• 13122 ÷ 18 = 729 (quotient)
• 729 = (9)³ [So, 729 is a perfect square]
• Which implies, 18 is the required smallest number by which 13122 should be divided in order to get a perfect cube as the quotient.

Hence, 18 is the required smallest number.