Question

Find the smallest number by which 16384 be divided so that the quotient may be a perfect square.

Answer 1

Answer:

The largest perfect cube smaller than 16,384 is 15,625. 15,625×1.048576=16,384.

That’s dangerous water, though, as it leads to looking at numbers smaller than 1, allowing your perfect cube quotient to become larger than 16,384, and we head off toward infinity. Negative numbers are something to consider too, since a cube can be negative, unlike a square. So maybe we stick to positive integers for everything.

The perfect cubes smaller than 16,384 are:

15,625 (25³)

13,824 (24³)

12,167 (23³)

10,648 (22³)

9,261 (21³)

8000 (20³)

6,859 (19³)

5,832 (18³)

4,913 (17³)

4,096 (16³) AH-HA!

16,384 ÷ 4,096 = 4, so 16,384 ÷ 4 = 4,096

4,096 is our perfect cube quotient, and the divisor of 16,384 is 4.