Prime Factorisation of Cube Numbers

Q.

What is the smallest number by which $392$ must be multiplied so that the product is a perfect cube?

1. $6$

2. $7$

3. $5$

4. $4$

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 by which 108 must be divided so that the quotient is a perfect cube?

1. 8
2. 4
3. 12
4. 15

Q. Express 3600 as a product of powers of their prime factors.

Q. Prime factorization of 343 is _____.

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

Q.

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

1. 24

2. 27

3. 44

4. 54

Q.

Question 46

Fill in the blanks to make the statements true.

The least number by which 72 be multiplied to make it a perfect cube is ___.

Q.

Question 13

Write the correct answer from the given four options.

Which of the following numbers is a perfect cube?

a) 243
b) 216
c) 392
d) 8640

Q.

Express 3375 in exponential form.

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

2. $3^3\times 5^2$

3. $3^3\times 5^3$

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

Q.

What should be multiplied with $a^3$ $b^2$ to make it a perfect cube? Given 'a' and 'b' are prime numbers.

1. $b$

2. $a^2$ $b$

3. $a^3$

4. $b^3$

Q. Find the smallest number by which $8788$ must be divided so that the quotient is a perfect cube.

Q. What is the smallest number by which 108 must be divided so that the quotient is a perfect cube?

1. 4
2. 15
3. 12
4. 8

Q. ${18}^3$ can be written as

1. $9^3\times 9^3$
2. $2^3\times 3^3\times 3^3$
3. $3^3\times 3^3\times 3^3$
4. $9^3\times 3^3$

Q.

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

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

1. 4
2. 7
3. 6
4. 2

Q.

How to make 256 a perfect cube?

1. Multiply by 4

2. Divided by 8

3. Multiply by 2

4. Divide by 2

Q. Write the greatest common factor of the following terms $3x^{2}y$, $18x{y}^2$, $-6xy$

Q. The smallest natural number by which $2401$ must be divided to get a perfect cube is?

1. $7$
2. $1$
3. $2$
4. $5$

Q.

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

1. 4

2. 6

3. 7

4. 2

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.

Find the smallest number by which 8788 must be divided so that the quotient will be a perfect cube.

1. 4

2. 3

3. 5

4. 6

Q. Write the greatest common factor of the following terms $2xy$, $-y^2$, $2xy$

Q. By what smallest number $29160$ be divided so that the quotient becomes a perfect cube?

Q.

When 81 is multiplied by a positive integer X, we get a perfect cube, then the value of X is:

1. 9

2. 81

3. 11

4. 8

Q.

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