Prime Factorisation Method to Find a Cube

Q.

Question 4
Parikshit makes a cuboid of plasticine of sides 5cm, 2cm, 5cm. How many such cuboids will he need to form a cube?

Q. Find the least number, which when divided by 12, 15, 20 and 54 leaves a remainder of 8 in each case.

1. 548
2. 484
3. 348
4. 644

Q.

Find the smallest number by which 2560 must be multiplied so that the product is a perfect cube.

Q.

Find the smallest number by which the following number must be divided to obtain a perfect cube:
$81$

Q.

Find the smallest number by which $1323$ must be multiplied so that the product is a perfect cube.

Q.

What is the smallest number by which 1600 must be divided so that the quotient is a perfect cube?

Q.

Which of the following numbers are perfect cubes? In case of perfect cube, find the number whose cube is the given number.
(i) 125 (ii) 243 (iii) 343 (iv) 256 (v) 8000 (vi) 9261 (vii) 5324 (viii) 3375

Q. The prime factorization of 648 =

1. 22x 34
2. 23x 34
3. 23x 35

Q.

Three numbers are in the ratio 1 : 2 : 3. The sum of their cubes is 98784. Find the numbers.

Q.

By what least number should 648 be multiplied to get a perfect cube?
(a) 3 (b) 6
(c) 9 (d) 8

Q.

Express $2160$ as the product of powers of their prime factors.

Q. Find the smallest number by which 100 should be multiplied to obtain a perfect cube.

Q. Is 392 a perfect cube? If not, find the smallest natural number by which 392 should be multiplied so that the product is a perfect cube.

Q.

What should be multiplied to 43200 to make it a perfect cube?

1. 2

2. 3

3. 5

4. Already a perfect cube

Q. Find the smallest number which when multiplied with 5184 will make the product a perfect cube.

1. 2
2. 6
3. 3
4. 9

Q.

Each prime factor appears 3 times in its cube. State whether the statement is true (T) or false (F).

1. True
2. False

Q.

Which of the following are perfect cubes ?
(i) 64 (ii) 216 (iii) 243 (iv) 1000 (v) 1728 (vi) 3087 (vii) 4608 (viii) 106480 (ix) 166375 (x) 456533

Q.

By what least number should 1536 be divided to get a perfect cube?
(a) 3 (b) 4
(c) 6 (d) 8

Q.

Question 81

State whether the following statement is true or false:

999 is a perfect cube.

Q.

Question 2(iii)
Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube:
72

Q. Is the long division method used for finding the cube roots?

Q.

Which of the following numbers is a perfect cube ?
(a) 1152 (b) 1331
(c) 2016 (d) 739

Q. What is the least number by which 6750 may be divided so that the quotient is a perfect cube?

A: 2

B: 3

C: 5

D: 6

$\left[1\right]$

Q. Show that -17576 is a perfect cube

Q.

Which of the following numbers is a perfect cube ?
(a) 141 (b) 294
(d) 216 (d) 496

Q.

Question 3(i)
You are told that 1, 331 is a perfect cube. Can you guess with factorization what is its cube root? Similarly guess the cube roots of 4913.

Q.

The sum of the cubes of two numbers is 35. The numbers are in the ratio of 2:3. Find the numbers.

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

Q.

Question 1(v)
State whether the number given below is a perfect cube or not:
46656

Q.

Find the smallest number by which the following number must be divided to obtain a perfect cube: $192$

Q.

Question 1(i)
State whether the number given below is a perfect cube or not.
216