What is the smallest number by which the following numbers must be multiplied, so that the products are perfect cubes?
(i) 675 (ii) 1323
(iii) 2560 (iv) 7803
(v) 107811 (vi) 35721
Factors of 675 = 3 × 3 × 3 × 5 × 5 = 33 × 52
Hence, to make a perfect cube we need to multiply the product by 5.
Factors of 1323 = 3 × 3 × 3 × 7 × 7 = 33 × 72
Hence, to make a perfect cube we need to multiply the product by 7.
Factors of 2560 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 = 23 × 23 × 23 × 5
Hence, to make a perfect cube we need to multiply the product by 5 × 5 = 25.
Factors of 7803 = 3 × 3 × 3 × 17 × 17 = 33 × 172
Hence, to make a perfect cube we need to multiply the product by 17.
Factors of 107811 = 3 × 3 × 3 × 3 × 11 × 11 × 11 = 33 × 3 × 113
Hence, to make a perfect cube we need to multiply the product by 3 × 3 = 9.
Factors of 35721 = 3 × 3 × 3 × 3 × 3 × 3 × 7 × 7 = 33 × 33 × 72
Hence, to make a perfect cube we need to multiply the product by 7.