Question

Find the smallest number by which 2400 be multiplied to make it a perfect cube

Answer 1

Hey

Refer to the attachment

hope this helps you

Answer 2

Given : The main number is 2400

To find : The smallest number by which 2400 be multiplied to make it a perfect cube.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to determine the necessary number)

In a perfect cube, all the prime factors are always in the groups of triples.

Now, we have to do prime factorisation of the given numbers.

So,

2400 = 2×2×2×2×2×3×5×5

or, 2400 = (2×2×2) × (2×2) × (3) × (5×5)

Now, in the above mentioned prime factorisation, there are three incomplete groups of triples. We have to complete those incomplete triples to make the main number a perfect cube.

By, competing the triples, we get :

(2×2×2) × (2×2×2) × (3×3×3) × (5×5×5) = 2400 × 2 × 3 × 3 × 5

(2×2×2) × (2×2×2) × (3×3×3) × (5×5×5) = 2400 × 90

Now,

• 2400 × 90 = 216000 = (60)³
• So, (2400×90) produces a perfect cube.

Hence, the smallest number number by which 2400 be multiplied to make it a perfect cube is 90