Question

100 - Find the smallest number by which the given number must be multiplied to obtain a perfect cube?

Answer 1

Hey there!

100 = 2 * 50

= 2 * 2 * 25

= 2² * 5²

So, To make the given number a perfect cube, You need to have one more 2 , 5 as part of its prime factorization.

2 * 5 = 10

The least number by which 100 be multiplied to get a perfect cube is 10 .

Multiplying 100 by 10 , you obtain 1000

whose prime factorization has triplets of 2 & 5

1000 = 2³ * 5³

Therefore, The smallest number by which the given number should be multiplied to obtain a perfect cube is 10

Answer 2

100 = 2×25×2
100 = 2×5×5×2
100 = 2^2×5^2

to get cube we need one 2 and one 5

2 × 5 = 10

multiply 100 with 10 we get ;

10 × 100 = 1000

2×5×25×4 = 1000

2×5×5×5×2×2 = 1000

2^3×5^3 = 1000

therefore...the smallest number by which the given number must be multiplied to obtain a perfect cube is 10

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