Question

Find the least number by which 11664 must be divided so as to make a quotient a perfect cube

Answer 1

:-)The answer is 4

Let’s find all the prime factors of the given number,

11664 = 2 x 5832

11664 = 2 x 2 x 2916

11664 = 2 x 2 x 2 x 1458

11664 = 2 x 2 x 2 x 2 x 729

11664 = 2 x 2 x 2 x 2 x 3 x 243

11664 = 2 x 2 x 2 x 2 x 3 x 3 x 81

Let me jump a few steps here

11664 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3

Now we make a Trio of similar numbers as,

11644 = (2 x 2 x 2) x (2) x (3 x 3 x 3) x (3 x 3 x 3)

We can see there is only 1 digit left out.

We can multiply it by a pair of same numbers i.e 2 to make the given number a Perfect Cube.

Thus the number if multiplied by 4 becomes a perfect cube (46656 = 36 x 36 x 36).

I HOPE IT HELPS