# Prime Factorisation

## Trending Questions

**Q.**

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

True

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:

6

2

3

4

**Q.**

Rahul makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. 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?

17 units

16 units

22 units

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 _______.

- 2
- 3
- 4
- 5

**Q.**

If the volume of a cube is 125 m^{3} then its side length is:

15

25

5

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?

18

12

36

6

**Q.**

Find the volume of a cube whose surface area is 486 cm^{2}.

**Q.**

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

**Q.**

Volume of a box is 2197 cm^{3} . 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?

9

15

25

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?

- 3
- 2
- 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 _____.

- 23
- 25
- 27
- 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 16x3 and 32x.

- 10
- 8
- 1
- 5

**Q.**

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