Prime Factorisation and Its Applications

The numbers \(1680\) and \(14\ 850\), expressed as the product of their prime factors, are \(1680 = 2^4 \times 3 \times 5 \times 7\) and \(14\ 850 = 2 \times 3^3 \times 5^2 \times 11\).

Hence, find

1. the largest integer which is a factor of \(1680\) and \(14\ 850\),
2. the smallest positive integer \(k\), such that \(14\ 850k\) is a perfect square,
3. the smallest positive integer \(m\), such that \(1680 \times 14\ 850 \times m\) is a perfect cube.