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

Ko‘paytma $12\cdot 30$ ni tub ko‘paytuvchilarga ajratamiz: $$12=2^{2}\cdot 3,\qquad 30=2\cdot 3\cdot 5.$$ Shunday qilib $$12\cdot30 = 2^{3}\cdot 3^{2}\cdot 5^{1}.$$ Agar son $n=p_{1}^{a_{1}}p_{2}^{a_{2}}\dots p_{k}^{a_{k}}$ ko‘rinishda bo‘lsa, uning natural bo‘luvchilar soni $$\tau (n)=(a_{1}+1)(a_{2}+1)\dots (a_{k}+1).$$ Bu yerda $a_{1}=3,\;a_{2}=2,\;a_{3}=1$, shuning uchun $$\tau (12\cdot30)=(3+1)(2+1)(1+1)=4\cdot3\cdot2=24.$$ Demak, $12\cdot30$ sonining natural bo‘luvchilar soni **24** ga teng.