Prime Factorization of Cube Numbers

Q.

Express $140$ as a product of its prime factor.

Q.

Express each number as a product of its prime factors: $3825$

Q.

Find the smallest number by which 27783 must be multiplied to get a perfect cube

1. 3

2. 9

3. 21

4. 49

Q. The smallest number by which 1080 should be divided to make it a perfect cube is

1. $3$
2. $4$
3. $5$
4. $2$

Q.

By what smallest number should $3600$ be multiplied so that the quotient is a perfect cube.

Also find the cube root of the quotient.

Q. To convert 16 to a perfect cube, the smallest number it should be mutiplied by is

1. 2
2. 4
3. 16
4. 8

Q.

Find the value of $\sqrt[3]{35}\times \sqrt[3]{350}\times \sqrt[3]{3500}$.

1. 500

2. 125

3. 50

4. 25

Q. Evaluate:

iii) $\sqrt[3]{3700\times 2\times 49\times 5}$

Q. Match the numbers with the number to be multiplied with to convert them into a perfect cube.

1. 3
2. 4
3. 2
4. 5

Q. should be multiplied with $a^3$ $b^2$ to make it a perfect cube, if a and b are prime numbers?

1. a${}^3$
2. a${}^2$b
3. b

Q. Which of the following is a perfect cube?

1. 297
2. 144
3. 2744
4. 218

Q.

How to make 256 a perfect cube?

1. Divide by 4

2. Divided by 8

3. Multiply by 2

4. Divide by 2

Q. To convert 16 to a perfect cube, the smallest number it should be mutiplied by is

1. 2
2. 4
3. 16
4. 8

Q. Is $2880$ a perfect cube? If not, by which smallest natural number should $2880$ be divided so that the quotient is a perfect cube?

Q.

By which smallest number should 42592 be divided so that the quotient is a perfect cube?

Q. Match the numbers with the number to be multiplied with to convert them into a perfect cube.

1. 3
2. 4
3. 2
4. 5

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.

What is the smallest number with which 1188 should be divided to get a perfect cube?

1. 44

2. 54

3. 27

4. 24

Q.

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

1. 6

2. 2

3. 4

4. 7

Q. By which smallest number must the following numbers be divided so that the quotient is a perfect cube?
$\left(i\right)675$

Q. What is the least number by which 10125 may be divided so that the quotient is a perfect cube?

1. 2
2. 3
3. 4
4. 5