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

Ko‘paytma $48\cdot70\cdot144$ ni tub bo‘luvchilarga ajratamiz: $48=2^{4}\cdot3$, $70=2\cdot5\cdot7$, $144=2^{4}\cdot3^{2}$. Bularni birga ko‘paytirib, umumiy darajalarni yig‘amiz: $48\cdot70\cdot144=2^{4+1+4}\cdot3^{1+2}\cdot5^{1}\cdot7^{1}=2^{9}\cdot3^{3}\cdot5\cdot7$. Agar bir son $n=p_{1}^{a_{1}}p_{2}^{a_{2}}\dots p_{k}^{a_{k}}$ shaklida bo‘lsa, uning natural bo‘luvchilari soni $\displaystyle (a_{1}+1)(a_{2}+1)\dots (a_{k}+1)$ ga teng. Bu yerda $a_{1}=9$, $a_{2}=3$, $a_{3}=1$, $a_{4}=1$, shuning uchun $\displaystyle (9+1)(3+1)(1+1)(1+1)=10\cdot4\cdot2\cdot2=160$. Demak, $48\cdot70\cdot144$ sonining natural bo‘luvchilari soni **160** ga teng.