Advertisements
Advertisements
Question
By which smallest number must the following number be divided so that the quotient is a perfect cube?
1600
Advertisements
Solution
On factorising 1600 into prime factors, we get:
\[1600 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5\]
On grouping the factors in triples of equal factors, we get:
\[1600 = \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times 5 \times 5\]
It is evident that the prime factors of 1600 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 1600 is a not perfect cube. However, if the number is divided by (\[5 \times 5 = 25\]), the factors can be grouped into triples of equal factors such that no factor is left over.
Thus, 1600 should be divided by 25 to make it a perfect cube.
RELATED QUESTIONS
Which of the following is perfect cube?
166375
What is the smallest number by which the following number must be multiplied, so that the products is perfect cube?
7803
By taking three different values of n verify the truth of the following statement:
If n leaves remainder 1 when divided by 3, then n3 also leaves 1 as remainder when divided by 3.
Write true (T) or false (F) for the following statement:
If a2 ends in an even number of zeros, then a3 ends in an odd number of zeros.
Show that the following integer is cube of negative integer. Also, find the integer whose cube is the given integer −2744000 .
Show that:
\[\frac{\sqrt[3]{729}}{\sqrt[3]{1000}} = \sqrt[3]{\frac{729}{1000}}\]
Find if the following number is a perfect cube.
1938
Find the smallest number by which 8768 must be divided so that the quotient is a perfect cube.
Find the cube-root of 250.047
If the cube of a squared number is 729, find the square root of that number
