Prime Factorisation

Q.

If LCM and HCF of two numbers are equal then, both the numbers are same and equal to LCM or HCF.

1. True

2. False

Q. How to know if a number is a perfect cube?

Q.

Find the smallest number by which 8640 must be divided so that quotient is a perfect cube

Q. Find the smallest number by which 704 must be divided to obtain a perfect cube.

Q. Find the smallest number by which 675 must be multiplied to obtain a perfect cube.

Q.

The least number that must be multiplied by 72 to make it a cube number is:

1. 6

2. 2

3. 3

4. 4

Q.

Rahul makes a cuboid of plasticine of sides $5cm,2cm,5cm$. How many such cuboids will he need to form a cube?

Q.

The area of a square tile is 324 square units. What is the length of each side of the tile?

1. 17 units

2. 16 units

3. 22 units

4. 18 units

Q.

Factorise: $x^2+xy+8x+8y$

Q.

What smallest number should 7803 be multiplied with so that product becomes a perfect cube

Q. The smallest number multiplied to 54, 000 to obtain a perfect cube is _______. ​

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

Q.

If the volume of a cube is 125 m³ then its side length is:

1. 15

2. 25

3. 5

4. 4

Q. Divide the number 26244 by the smallest number so that the quotient is a perfect cube. Also, find the cube root of the quotient. [4 MARKS]

Q.

Find the smallest number(s) by which $3087,33275,120393$ must be divided respectively so that quotient is a perfect cube.

Q.

The length, breadth and height of a cuboid are 18 cm, 6 cm and 12 cm respectively. How many such cuboids will be required to make a cube?

1. 18

2. 12

3. 36

4. 6

Q.

Find the volume of a cube whose surface area is 486 cm².

Q.

Find the cube roots of the following perfect cubes using estimation 592704

Q.

Volume of a box is 2197 cm³ . The length of its side is ___________.

Q.

What is the smallest number by which 1125 may be divided so that the quotient is a perfect cube?

1. 9

2. 15

3. 25

4. 3

Q. Find the smallest number by which 128 must be divided to obtain a perfect cube.

Q.

Anshul and Balendu have 50 cubes of side 1 cm. They decided to make a larger cube by joining these smaller cubes. The number of larger cubes (all of different sizes) they can make is

___

Q. Find the smallest number by which 3136 must be multiplied.

Q.

Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube.

(i) 81

(ii) 128

(iii) 135

(iv) 192

(v) 704

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

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

Q.

How can we find the perfect cube and what is a perfect cube

Q. What is the smallest number by which 1375 should be divided so that the quotient may be a perfect cube?

Q. The sum of prime factors of 1575 is _____.

1. 23
2. 25
3. 27
4. 20

Q.

The least number by which$72$ be divided to make it a perfect cube is _____________.

Q. Find the number of common factors of $16x^3$ and $32x$.

1. 10
2. 8
3. 1
4. 5

Q.

Shishir is making a cube of side 6cm using cubes of side 2cm. How many such cubes are needed.