Bo'linuvchanlik. Sonning natural bo'luvchilar soni va yig'indisi bo‘yicha savol

If $n=2^{3}\cdot 3^{m}$, then any divisor of $n$ is of the form $2^{a}\,3^{b}$ where $0\le a\le3$ and $0\le b\le m$. Shu sababli, bo‘luvchilar soni \((3+1)(m+1)=4(m+1)\) ga teng bo‘ladi. Berilgan shart bo‘yicha bu son $20$ ga teng: \[ 4(m+1)=20\;\Longrightarrow\;m+1=5\;\Longrightarrow\;m=4. \] Demak, $m$ ning qiymati **4** ga teng, ya'ni javob **A**.