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

100 sonining natural bo‘luvchilarini topish uchun avvalo uning tub ko‘paytuvchini ajratamiz: $100 = 2^{2}\cdot 5^{2}$. Agar $n = p_{1}^{a_{1}}\cdot p_{2}^{a_{2}}\cdots p_{k}^{a_{k}}$ bo‘lsa, $n$ ning natural bo‘luvchilar soni $\displaystyle (a_{1}+1)(a_{2}+1)\cdots (a_{k}+1)$ ga teng. Bu holda $a_{1}=a_{2}=2$, shuning uchun bo‘luvchilar soni $\displaystyle (2+1)(2+1)=3\cdot 3=9$. Demak, 100 sonining natural bo‘luvchilar soni **9** ga teng, ya'ni javob **D**.