Question

By which smallest number 13122 must be divided, so that the quotient is a perfect cube?​

Answer 1

Answer:

Hii

Divide the number 13122 by the smallest number so that the quotient is a perfect cube - Brainly.in.

Divide the number 13122 by the smallest number so that the quotient is a perfect cube - Brainly.in.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)

Answer 2

Given: the number is 35721

To find: what is the smallest number by which 35721 must be divided so that the quotient is a perfect cube

Solution:

35721 = 3 × 11907

= 3 × 3 × 3969

= 3 × 3 × 3 × 1323

= 3 × 3 × 3 × 3 × 441

= 3 × 3 × 3 × 3 × 3 × 147

= 3 × 3 × 3 × 3 × 3 × 3 × 49

= 3 × 3 × 3 × 3 × 3 × 3 × 7 × 7

We see that, in prime factorization of 35721, three 3s exist twice and 7s exist two times only.

If we divide the number 35721 by two 7s, i.e., 7 × 7 = 49, then the numebr will become a perfect cube.

Answer: 49 is the smallest number by which 35721 must be divided so that the quotient is a perfect cube.