Cube root of 1728 by using prime factorization method

Learn how to get the answer for the cube root of 1728 using prime factorization method. This method will be very simple and also easy to understand. Now let’s see how to proceed for finding the cube root of 1728 value by prime factorization. Remember that while doing factorization you should use only prime numbers.

Cube root of 1728 by using prime factorization method

First thing is that we need to write given number i.e. 1728 as a product of prime numbers. In order to write 1728 as a product of primes, we need to do factorization. Now let’s proceed with the factorization of 1728.

The Process of Prime factorization to find the cube root of 1728 is given below:

Write 1728 as shown in below figure.

Take the first prime number 2 and write left of 1728 as shown in the figure.

Cube root of 1728 by using prime factorization methodIn 2nd table 1728 goes 864 times so below 1728 write 864.

Cube root of 1728 by using prime factorization method

Now again take the 2nd table and divide 864 by it.

In 2nd table 864 goes 432 times so write it down of 864.

Cube root of 1728 by using prime factorization method

As the number 432 is divisible by 2 now once again take 2.

Divide 432 by 2 you will get 216.

So write 216 below 432.

Cube root of 1728 by using prime factorization method

 

As 216 is divisible by the number 2 so take once again 2.

Divide 216 by 2 the result will be 108.

So write 108 below 216.

Cube root of 1728 by using prime factorization method

Again take 2 as 108 is divisible by 2.

Divide 108 by 2 then the result is 54.

Write down below 108.

Cube root of 1728 by using prime factorization method

As 54 is divisible by 2 take 2 and divide it.

The result is 27. So write down below 54.

Cube root of 1728 by using prime factorization method

Now 27 is not divisible by 2 so take next prime number 3.

Now divide the number 27 by 3 and the result equals to 9. Write 9 below 27.

Cube root of 1728 by using prime factorization method

 

Now the number 9 is divisible by 3 so take 3 and divide it.

The result is 3. Write 3 below 9.

Cube root of 1728 by using prime factorization method

As 3 is divisible by 3 so take that prime number.

Divide 3 by 3 result is 1.

Write below 3.

Cube root of 1728 by using prime factorization method

At last now we have done Prime factorization of the number 1728.

Now

               1728 = 2 × 2 × 2 × 2 × 2 × 2 ×3 × 3 × 3

Then group them by three same numbers and mark it as a bar as shown below.

Cube root of 1728 by using prime factorization method

Now if you observe we have, know 3 groups.

For the first group write one 2 and for the second group write one more 2 and for the last group write one 3.

Multiply all these and the result will be answer for cube root of 1728 i.e. 2 × 2 × 3 = 12

So, finally the cube root of 1728 = 12.