$1\cdot 2\cdot 3\cdot \ldots \cdot 249\cdot 250$ ko'paytmasi nechta 0 raqami bilan tugaydi?
- A. 66
- B. 62
- C. 59
- D. 57
Bo'linuvchanlik. Sonning natural bo'luvchilar soni va yig'indisi bo‘yicha savol
Javob va yechimni ko‘rish
Javob: 62
Ko‘paytma $1\cdot2\cdot3\cdots250$ – bu $250!$ (250 faktorial) ga teng.
0 raqami har safar “10” ga bo‘linish natijasida paydo bo‘ladi, ya’ni har bir $2$ va $5$ juftligi bitta 0 beradi. Shuning uchun $250!$ ning oxirgi 0 lar soni $250!$ ichidagi $2$ lar va $5$ lar juftliklaridan kichik bo‘lgan soniga teng.
$\displaystyle\text{Soni}(5)=\Big\lfloor\frac{250}{5}\Big\rfloor+\Big\lfloor\frac{250}{5^{2}}\Big\rfloor+\Big\lfloor\frac{250}{5^{3}}\Big\rfloor
=50+10+2=62.$
$\displaystyle\text{Soni}(2)=\Big\lfloor\frac{250}{2}\Big\rfloor+\Big\lfloor\frac{250}{2^{2}}\Big\rfloor+\Big\lfloor\frac{250}{2^{3}}\Big\rfloor+\dots
=125+62+31+15+7+3+1=244.$
$2$ lar soni $5$ lar sonidan ko‘proq bo‘lgani sababli, 0 lar soni $5$ lar soni bilan belgilanadi, ya’ni $62$.
Shu bois $1\cdot2\cdot\ldots\cdot250$ ko‘paytmasi **62 ta** 0 bilan tugaydi. (Javob B).
Mavzuni mustahkamlang
Bu savol Bo'linuvchanlik. Sonning natural bo'luvchilar soni va yig'indisi mavzusiga tegishli. Ta’riflar, formulalar va misollarni mavzu sahifasida ko‘ring.
Mavzuni o‘rganish