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

Ko‘paytma $4\cdot5\cdot6\cdot7\cdot8\cdot9\cdot10$ ni tub ko‘rinishga ajratamiz. \[ \begin{aligned} 4 &=2^{2},\\ 5 &=5,\\ 6 &=2\cdot3,\\ 7 &=7,\\ 8 &=2^{3},\\ 9 &=3^{2},\\ 10&=2\cdot5. \end{aligned} \] Bularni birga qo‘shsak, umumiy ko‘paytma \[ 2^{2+1+3+1}=2^{7},\qquad 3^{1+2}=3^{3},\qquad 5^{1+1}=5^{2},\qquad 7^{1}=7. \] Demak, sonning tub ko‘rinishi $2^{7}\,3^{3}\,5^{2}\,7^{1}$ ga teng. Natural bo‘luvchilar soni har bir eksponentga $1$ qo‘shib, ko‘paytmasi: \[ (7+1)(3+1)(2+1)(1+1)=8\cdot4\cdot3\cdot2=192. \] Shunday qilib, bu sonning natural bo‘luvchilar soni $\boxed{192}$.