Question

Find the smallest number by which 17496must be divided,so that the quotient is perfect cube . Also find the cube root of the quotient.

Answer 1

Answer:

17496 = 2 * 2 * 2 * 3 *3 * 3 * 3 * 3 * 3 * 3

• Since 2 and 3 are left out without any pair divide
• 17496 with 2 or 3
• 17496/2 = 8748 ( quotient)
• 8748 has no perfect cube root
• Hence we will consider 3
• 17496/3 = 5832
• cube root of 5832 = 18

Therefore , 3 is the smallest number with which 17496 is divided ,so that the quotient will be perfect cube root