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

360 sonini tub ko‘paytuvchilarga ajrating: $360 = 2^{3}\cdot 3^{2}\cdot 5^{1}$. Agar $n=p_{1}^{a_{1}}p_{2}^{a_{2}}\dots p_{k}^{a_{k}}$ bo‘lsa, $n$ ning natural bo‘luvchilar soni $(a_{1}+1)(a_{2}+1)\dots (a_{k}+1)$ ga teng. Demak, $360$ ning bo‘luvchilar soni $(3+1)(2+1)(1+1)=4\cdot 3\cdot 2=24$. Javob: **A) 24**.