Factors of many

We can show that

$\left( \begin{matrix} 120 \\ 6 \end{matrix} \right) =\frac { 120 }{ 6 } \left( \frac { 120 }{ 1 } -1 \right) \left( \frac { 120 }{ 2 } -1 \right) \left( \frac { 120 }{ 3 } -1 \right) \left( \frac { 120 }{ 4 } -1 \right) \left( \frac { 120 }{ 5 } -1 \right)$

$\frac { 120 }{ 6 } \left( \frac { 120 }{ 1 } -1 \right) \left( \frac { 120 }{ 2 } -1 \right) \left( \frac { 120 }{ 3 } -1 \right) \left( \frac { 120 }{ 4 } -1 \right) \left( \frac { 120 }{ 5 } -1 \right) =20\times 119\times 59\times 39\times 29\times 23$

$20={ 2 }^{ 2 }\times 5$

$119=7\times 17$

$39=3\times 13$

the other are all prime numbers so,

${ 2 }^{ 2 }\times 3\times 5\times 7\times 13\times 17\times 23\times 29\times 59$

$3\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=\boxed { 768 }$