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

Berilgan sonni tub ko‘paytuvchilarga ajrating: $100=2^{2}\cdot5^{2}$, $198=2\cdot3^{2}\cdot11$, $324=2^{2}\cdot3^{4}$. Shu bilan $100\cdot198\cdot324=2^{5}\cdot3^{6}\cdot5^{2}\cdot11$. Agar $n=p_{1}^{a_{1}}p_{2}^{a_{2}}\dots p_{k}^{a_{k}}$ bo‘lsa, $n$ ning natural bo‘luvchilari soni $\displaystyle (a_{1}+1)(a_{2}+1)\dots (a_{k}+1)$. Bu holda $(5+1)(6+1)(2+1)(1+1)=6\cdot7\cdot3\cdot2=252$. Demak, to‘g‘ri javob **C) 252**.