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.

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.

In 2^{nd} table 1728 goes 864 times so below 1728 write 864.

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

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

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.

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.

Again take 2 as 108 is divisible by 2.

Divide 108 by 2 then the result is 54.

Write down below 108.

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

The result is 27. So write down below 54.

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.

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

The result is 3. Write 3 below 9.

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

Divide 3 by 3 result is 1.

Write below 3.

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.

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.

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