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What is the greatest prime factor of 1+2+3+。。。+40?

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What is the greatest prime factor of 1+2+3+。。。+40?  [#permalink]

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New post Updated on: 19 Jun 2016, 18:06
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What is the greatest prime factor of 1+2+3+。。。+40?
A. 17
B. 29
C. 31
D. 37
E. 41

*An answer will be posted in 2 days.

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Originally posted by MathRevolution on 18 Jun 2016, 00:27.
Last edited by MathRevolution on 19 Jun 2016, 18:06, edited 1 time in total.
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Re: What is the greatest prime factor of 1+2+3+。。。+40?  [#permalink]

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New post 18 Jun 2016, 00:35
1
I dont understand this

Sum = n(n+1)/2
Sum = 40*41/2 = 820
41 divides 820 evenly making E the answer.
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Re: What is the greatest prime factor of 1+2+3+。。。+40?  [#permalink]

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New post 18 Jun 2016, 01:05
MathRevolution wrote:
What is the greatest prime factor of 1+2+3+。。。+40?
A. 17
B. 29
C. 31
D. 37
E. 41

*An answer will be posted in 2 days.



HI,

find the sum from direct formula = n(n+1)/2 = 40(40+1)/2 = 20*41...
41 is a PRIME number, so ans is 41..

A is wrong ....E is the answer
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Re: What is the greatest prime factor of 1+2+3+。。。+40?  [#permalink]

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New post 18 Jun 2016, 01:15
With Chetan

Answer must be (E) 41

Sume of the series is 820

Further \(820\)= \(2^2\) x \(5^1\) x \(41^1\)

So, 820 must be divisible by 41 which is the greatest prime factor of the series.


MathRevolution

Please recheck and confirm the correct answer...
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Re: What is the greatest prime factor of 1+2+3+。。。+40?  [#permalink]

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New post 19 Jun 2016, 18:08
I am so sorry! I made a mistake, the correct answer is E. I will post the solution tomorrow!

Thank you.
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Re: What is the greatest prime factor of 1+2+3+。。。+40?  [#permalink]

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New post 19 Jun 2016, 23:30
Sum will be 41 * 20 , so greatest prime factor will be 41.

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Re: What is the greatest prime factor of 1+2+3+。。。+40?  [#permalink]

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New post 20 Jun 2016, 17:31
We can calculate 1+2+3+…..+n=n(n+1)/2. Then, 1+2+3+。。。+40=40(40+1)/2=20(41)=(2^2)(5)(41). Hence, the biggest prime factor is 41 and the correct answer is E.
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Re: What is the greatest prime factor of 1+2+3+。。。+40?  [#permalink]

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New post 22 Nov 2016, 02:03
Here N=> Sum of first 40 positive integers
N=40/2(1+40)
N=20*41
Clearly greatest Prime factor =41

Alternatively
Mean of an Ap series is the average of the first and the last term=(1+40)/2
Mena = 41/2
Sum/number of terms = mean
Sum = mean * 40
(41/2)*40 = N
N=20*41

Hence E
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Re: What is the greatest prime factor of 1+2+3+。。。+40?  [#permalink]

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New post 25 Nov 2016, 05:38
1+2+3+。。。+40= (41*40)/2=41*20

So the greatest prime factor is definitely 41 ;)

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Re: What is the greatest prime factor of 1+2+3+。。。+40?  [#permalink]

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Re: What is the greatest prime factor of 1+2+3+。。。+40?   [#permalink] 28 Jan 2019, 13:12
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