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Find the greatest prime divisor of the value of the arithmetic series
1 + 2 + 3 + \dots + 200

 Jun 23, 2024
 #1
avatar+85 
+1

1+2+3...198+199+200 is 50*201 since you can pair up the first and last, 2nd and 2nd to last, etc. 

201 is 3*67 and 50 is 2*5^2. the greatest prime factor is \(\boxed{ 67}\) :P

 Jun 23, 2024
 #2
avatar+1075 
+1

So, in order to calculate the list, we can use a handy trick. We simply take the largest number, multiply it by that number +1, and divide by 2. 

We have

\(\frac{200 \cdot 201}{2}=20100\)

 

The prime factorization of \(20100\) is 

\(20100 = 2^2 \cdot 3 \cdot 5^2 \cdot 67\)

 

Thus, the greatest prime divisor is 67. 

 

Thanks! :)

 Jun 23, 2024

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