Question

find the smallest number by which the following numbers must be multiplied so that the product is a perfect cube 1323, 2560​

Answer 1

Answer:

Using Prime factorisation for 1323

we get the following factors

(3×3×3) ×7×7

we can see that 3 is making the triplet but 7 doesn't

{ triplet is because question is asking us for the perfect cube }

so we need one 7 more to complete the triplet , therefore 7 is the smallest number which is needed to multiply with 1323 to get a perfect cube.

similarly

factors of 2560 is

(2×2×2)×(2×2×2)×(2×2×2)×5

here we need two 5's so 5×5 =25 is the smallest number