Question

Find the least number must be multiplied from 11664​

Answer 1

Answer:

What smallest number should be multiplied to 11664 to make it a perfect cube?  

So, you want the smallest umber that, when multiplied by 11664, gives a perfect square.

I note that most people have given 4. But there are better candidates.

How about zero? After all, 0 < 4! 0 times 11664 = 0 = 0 cubed.

Better yet, as Stephen Jones suggested, is -4, as -4 < 0

−4×11664=−46656=(−36)3  

Better yet, how about -136,048,896 (= -11,664 times 11,664), which is certainly less than -4.

−136048896×11664=−1×116643=(−11664)3

Better yet, how about -136,048,896,000 (= -116,640 times 116,640 times 10), which is certainly less than -136,048,896

−136048896000×11664=−1×1166403=(−116640)3  

We could keeping multiplying our negative number by multiples of 1,000 until the end of time and still we wouldn’t have got to the smallest number

Answer 2

Answer:

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).

hope it helps you friend.......