Question

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

Answer 1

Answer:

The smallest number is 7.

Solution:

To find the ‘smallest number’ by which 1323 will be multiplied, we need to factorize 1323 as under:

1323=3 \times 4411323=3×441

1323=3 \times 3 \times 1471323=3×3×147

1323=3 \times 3 \times 3 \times 491323=3×3×3×49

1323=3 \times 3 \times 3 \times 7 \times 71323=3×3×3×7×7

The above can be written as 1323=3^{3} \times 7^{2}.1323=3

3

×7

2

.

Now, 7 is not in triplet. If 7 is in triplet, then derived number will be perfect cube.

Hence, 1323 must be ‘multiplied by 7’ to get a ‘perfect cube’ as shown below:

1323=3^{3} \times 7^{3}=21 \times 21 \times 21=92611323=3

3

×7

3

=21×21×21=9261 .

Step-by-step explanation:

• hope it helps you!

Answer 2

Answer:

Prime factorising 1323, we get,

1323=3×3×3×7×7

$= {3}^{3} \times {7}^{2} .$

We know, a perfect cube has multiples of 3 as powers of prime factors.

Here, number of 3's is 3 and number of 7's is 2.

So we need to multiply another 7 in the factorization to make 1323 a perfect cube.

Hence, the smallest number by which 1323 must be multiplied to obtain a perfect cube is 7.