What is the smallest number by which 1600 must be divided so that the quotient is a perfect cube?
Let’s find out the prime factors of the given number,
2 | 1600 |
2 | 800 |
2 | 400 |
2 | 200 |
2 | 100 |
2 | 50 |
5 | 25 |
5 | 5 |
1 |
1600 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5
So, in these two pairs of 2 triplets, two 5 are extra. Therefore to get the perfect cube we have to divide the given number by 5×5, which is 25.