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

96 sonini tub ko‘paytmalariga ajrating: $96 = 2^{5}\cdot 3^{1}$. Agar $n = p_{1}^{a_{1}}p_{2}^{a_{2}}\dots p_{k}^{a_{k}}$ bo‘lsa, uning natural bo‘luvchilar soni $\displaystyle (a_{1}+1)(a_{2}+1)\dots(a_{k}+1)$ ga teng. Bu yerda $a_{1}=5$ va $a_{2}=1$, shuning uchun $$\text{bo‘luvchilar soni}= (5+1)(1+1)=6\cdot2=12.$$ Demak, 96 sonining natural bo‘luvchilari soni **12** ga teng, ya’ni javob **A**.