Question

Find the smallest number by which 10640 must be multiplied to get a perfect cube

Answer 1

Number 10640 would be perfect cube if we multiply it to 1768900.

Step-by-step explanation:

• This can be found out very easily.

• To solve such types of problems, first we break the given numbers in the form of prime factors.

• 10640 = $2\times 2\times 2\times 2\times 5\times 7\times 19$

• Further, we can write as;

• 10640 = $2^3\times 2\times 5\times 7\times 19$

• Here, we can understand that this number would be perfect cube, if we would be able to write as;

• $2^3\times 2\times 2^2\times 5\times 5^2\times 7\times 7^2\times 19\times 19^2$

• But, it is not so.

Thus, we can say that number 10640 would be perfect cube if we multiply it to $2^2 \times 5^2 \times 7^2 \times 19^2$ = 1768900