The ifactors function returns the complete integer factorization of the integer or fraction n.

The result is returned as in the form $\left[u\,\left[\left[p_1\,e_1\right]\,\mathrm{...}\,\left[p_m\,e_m\right]\right]\right]$ where $n\=u{p}_1^{e_1}\cdots p_m^{e_m}$, $p_i$ is a prime integer, $e_i$ is its exponent (multiplicity) and u is the sign of n.

This function supports the same options as ifactor.

$\mathrm{ifactors}\left(61\right)$

$\left[1\,\left[\left[61\,1\right]\right]\right]$

$\mathrm{ifactors}\left(-120\right)$

$\left[\mathrm{-1}\,\left[\left[2\,3\right]\,\left[3\,1\right]\,\left[5\,1\right]\right]\right]$

$\mathrm{ifactors}\left(\frac{3}{4}\right)$

$\left[1\,\left[\left[2\,\mathrm{-2}\right]\,\left[3\,1\right]\right]\right]$

$\mathrm{ifactors}\left(0\right)$

$\left[0\,\left[\right]\right]$

$\mathrm{ifactors}\left(1\right)$

$\left[1\,\left[\right]\right]$

$\mathrm{ifactors}\left(1690575565024346828676664200680\,\mathrm{easy}\right)$

$\left[1\,\left[\left[2\,3\right]\,\left[5\,1\right]\,\left[17\,2\right]\,\left[\mathrm{\_c27\_1}\,1\right]\right]\right]$