Question

3. Find the smallest number by which each of the following numbers must be dividing
obtain a perfect cube.
(i) 81
(ii) 128
(i) 135
(iv) 192
(v) 704​

Answer 1

• 81 =3*3*3*3
• Here3 cannot appear in the group of triplets
• The smallest number number to be divided is 3
• 128=2*2*2*2*2*2*2
• Here 2 cannot appear in the group of triplets
• Therefore the smallest number to be divided is 2
• 135=3*3*3*5
• Here 5 cannot appear in the group of triplets
• The smallest no to be divided is 5
• 192 =2*2*2*2*2*2*3
• Here 3 cannot appear in the group of triplets
• Therefore the smallest number to be divided is 3
• 704=2*2*2*2*2*2*11
• Here 11 cannot appear in the group of triplets
• Therefore the smallest number to be divided is 11