Prime Factorisation Method to Find a Cube

Q. $\text{Which of the following numbers is not a perfect cube?}$

1. $1331$
2. $625$
3. $343$
4. $729$

Q.

If 6655 is divided by __, we get a perfect cube number.

Q.

The smallest number that is to be multiplied with 6655 so that the product will be a perfect cube is ___.

Q. 2744 written as a product of its primes is

1. $2\times 2\times 2\times 7\times 7$ ​
2. $2\times 2\times 7\times 7\times 7$
3. $2\times 2\times 7\times 7$
4. $2\times 2\times 2\times 7\times 7\times 7$

Q.

What is the minimum number we need to multiply with 392 to make it a perfect cube?

1. 6

2. 4

3. 7

4. 2

Q.

How many times the number 3 should be mutiplied with 648, in order to make it a perfect cube?

___

Q. The prime factorization of 648 is

1. $2^2\times 3^4$
2. $2^3\times 3^4$
3. $2^3\times 3^5$
4. $2^3\times 3^6$

Q. The prime factorization of 392 is

1. $2^2\times 5^4$
2. $2^3\times 3^5$
3. $2^3\times 7^2$
4. $2^3\times 7^3$

Q.

What is the minimum number that should be multiplied with 360 in order to make it a perfect cube ?

1. 65

2. 80

3. 75

4. 70

Q.

If a and b are coprime, what should $a^3$ $b^2$ be multiplied with to make it a perfect cube?

1. $a^2$ $b$

2. $a^3$

3. $b^3$

4. $b$