Question

descompunerea numerelor naturale de putere prima 508,2040,1116,3886,4250,5620,4800,84.000,4900,630,9800. ​

Answer 1

Răspuns:

• $\purple{\bf 508 = 2^{2} \cdot 127}$
• $\blue{\bf 2040 = 2^{3} \cdot 3\cdot5\cdot 17}$
• $\green{\bf 1116 = 2^{2} \cdot 3\cdot31}$
• $\red{\bf 38868 = 2\cdot 29\cdot67}$
• $~\pink{\bf 4250 = 2 \cdot 5^{3}\cdot17}$
• $~\purple{\bf 5620 = 2^2 \cdot 5\cdot281}$
• $\blue{\bf 2040 = 2^{3} \cdot 3\cdot5\cdot 17}$
• $\green{\bf 84000 = 2^{5} \cdot 3\cdot 5^{3}\cdot7}$
• $\red{\bf 4900 = 2^{2} \cdot 5^{2}\cdot7^2}$
• $\purple{\bf 9800 = 2^{3} \cdot 5^{2}\cdot7^2}$

Explicație pas cu pas:

✳️Numerele prime sunt acele numere care au exact doi divizori, numărul 1 și numărul în cauză

Câteva numere prime: 2, 3, 5, 7, 11, 13, 17, 19, 23, etc. ......

$\bf 508~\Big|~2\\254~\Big|~2\\~127~\Big|~127\\\underline{~\,~~1~\Big|~1~~}\\\\\Rightarrow ~\purple{\boxed{\bf 508 = 2^{2} \cdot 127}}$

$\it~$

$\bf 2040~\Big|~2\\1020~\Big|~2\\~\,~510~\Big|~2\\~\,~255~\Big|~3\\~~~~85~\Big|~5\\~~~~17~\Big|~17\\\underline{~\,~~~1~\Big|~1~~}\\\\\Rightarrow ~\blue{\boxed{\bf 2040 = 2^{3} \cdot 3\cdot5\cdot 17}}$

$\it~$  

$\bf 1116~\Big|~2\\~~~558~\Big|~2\\~~~279~\Big|~3\\~~\,~~93~\Big|~3\\~\,~~~31~\Big|~31\\\underline{~\,~\,~~1~\Big|~1~~~}\\\\\Rightarrow ~\green{\boxed{\bf 1116 = 2^{2} \cdot 3\cdot31}}$                

$\it ~$                              

$\bf 3886~\Big|~2\\1943~\Big|~29\\~~~~\,67~\Big|~67\\\underline{~\,~~~~1~\Big|~1~~~}\\\\\Rightarrow ~\red{\boxed{\bf 38868 = 2\cdot 29\cdot67}}$

$\bf 4250~\Big|~2\\~2125~\Big|~5\\~~~425~\Big|~5\\~~\,~~85~\Big|~5\\~\,~~~17~\Big|~17\\\underline{~\,~\,~~1~\Big|~1~~~~}\\\\\Rightarrow ~\pink{\boxed{\bf 4250 = 2 \cdot 5^{3}\cdot17}}$

 

$\bf 5620~\Big|~2\\~2810~\Big|~2\\~1405~\Big|~5\\~~~281~\Big|~281\\\underline{~~~\,~~1~\Big|~1~~~}\\\\\Rightarrow ~\purple{\boxed{\bf 5620 = 2^2 \cdot 5\cdot281}}$

$\bf 4800~\Big|~2\\2400~\Big|~2\\~1200~\Big|~2\\~~\,\,600~\Big|~3\\~~\,\,300~\Big|~5\\~\,\,~150~\Big|~2\\~~\,~~75~\Big|~3\\~~\,~~25~\Big|~5\\~~~~\,~~5~\Big|~5\\\underline{~\,~~~~1~\Big|~1~~~~}\\\\\Rightarrow ~\blue{\boxed{\bf 2040 = 2^{3} \cdot 3\cdot5\cdot 17}}$  

$\it~$

$\bf 84000~\Big|~2\\42000~\Big|~2\\~21000~\Big|~2\\~10500~\Big|~2\\~~\,5250~\Big|~2\\~~\,2625~\Big|~3\\~~~~875~\Big|~5\\~~~~175~\Big|~5\\~~~~~~35~\Big|~5\\~~~~\,~~~7~\Big|~7\\\underline{~~~~\,~~1~\Big|~1~~~~}\\\\\Rightarrow ~\green{\boxed{\bf 84000 = 2^{5} \cdot 3\cdot 5^{3}\cdot7}}$

$\it~$

$\bf4900~\Big|~2\\2450~\Big|~2\\~1225~\Big|~5\\~~~245~\Big|~5\\~\,~~~49~\Big|~7\\~~~~~~7~\Big|~7\\\underline{~~~~~1~\Big|~1~~~~}\\\\\Rightarrow ~\red{\boxed{\bf 4900 = 2^{2} \cdot 5^{2}\cdot7^2}}$

$\it~$

$\bf 630~\Big|~2\\315~\Big|~3\\~105~\Big|~3\\~~~35~\Big|~5\\~~~~~7~\Big|~7\\\underline{~~~~1~\Big|~1~~}\\\\\Rightarrow ~\pink{\boxed{\bf 630 = 2 \cdot 3^{2}\cdot5\cdot7}}$$\it~$

$\it~$  

$\bf 9800~\Big|~2\\4900~\Big|~2\\2450~\Big|~2\\~1225~\Big|~5\\~~\,\,245~\Big|~5\\\,~~\,~~49~\Big|~7\\~~~~~~7~\Big|~7\\\underline{~~~~~1~\Big|~1~~~}\\\\\Rightarrow ~\purple{\boxed{\bf 9800 = 2^{3} \cdot 5^{2}\cdot7^2}}$                

În link-urile de mai jos ai câteva exerciții asemănătoare ce te vor ajuta

https://brainly.ro/tema/158039

https://brainly.ro/tema/9119916

https://brainly.ro/tema/9345322

==pav38==

Baftă multă !