Question

Find the number of factors of the four-digit number which is a square as well as a cube.

Answer 1

Any number which can be written in the form a⁶ is a perfect square as well as a perfect cube, for any whole number a.

1⁶ = 1³ = 1² = 1

2⁶ = 4³ = 8² = 64

3⁶ = 9³ = 27² = 729

Thus, the four digit number mentioned in the question is 4⁶ = 16³ = 64² = 4096.

Prime factorization form of 4096 is 2¹².

So, 4096 has 13 factors.