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If n is the sum of the first 40 positive integers, what is the greates

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If n is the sum of the first 40 positive integers, what is the greates  [#permalink]

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New post 08 Jun 2017, 12:52
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If n is the sum of the first 40 positive integers, what is the greatest prime factor of n?

A. 29
B. 37
C. 41
D. 17
E. 19

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If n is the sum of the first 40 positive integers, what is the greates  [#permalink]

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New post 08 Jun 2017, 14:02
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Smokeybear00 wrote:
If n is the sum of the first 40 positive integers, what is the greatest prime factor of n?

A. 29
B. 37
C. 41
D. 17
E. 19

Nice question.

Sum of consecutive integers =

\(\frac{(First Term + Last Term)*(n)}{2}\), where n = number of terms

The first term is 1. The last term is 40.

Using the formula above, the sum is

\(\frac{(1 + 40)*(40)}{2}\)

=(41)(40) / 2

Stop there. 41 is a factor of the sum, and 41 is prime.

Answer C
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Re: If n is the sum of the first 40 positive integers, what is the greates  [#permalink]

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New post 08 Jun 2017, 14:48
Top Contributor
Smokeybear00 wrote:
If n is the sum of the first 40 positive integers, what is the greatest prime factor of n?

A. 29
B. 37
C. 41
D. 17
E. 19


Another useful formula: 1 + 2 + 3 + 4 + 5 + . . . .+ k = (k)(k+1)/2
So, for example, 1 + 2 + 3 + 4 + .... + 10 = (10)(10 + 1)/2 = 110/2 = 55

n = 1 + 2 + 3 + 4 + 5 + . . . .+ 40
= (40)(40 + 1)/2
= (40)(41)/2
= (20)(41)
At this point, we can see that 41 will be the greatest prime factor of n.
Answer:

For "fun" let's finish the prime factorization of n.
We left off at: n = (20)(41)
Continue to get: n = (2)(2)(5)(41)

Cheers,
Brent
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Re: If n is the sum of the first 40 positive integers, what is the greates  [#permalink]

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New post 31 Aug 2017, 05:39
Smokeybear00 wrote:
If n is the sum of the first 40 positive integers, what is the greatest prime factor of n?

A. 29
B. 37
C. 41
D. 17
E. 19


n = 1+2+3+4+..... + 40
= 40*41/2 = 20*41

So, greatest prime factor of n = 41
Answer C
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Re: If n is the sum of the first 40 positive integers, what is the greates  [#permalink]

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New post 29 Oct 2018, 14:35
Smokeybear00 wrote:
If n is the sum of the first 40 positive integers, what is the greatest prime factor of n?

A. 29
B. 37
C. 41
D. 17
E. 19


(40+1)/2=20.5 mean→
40*20.5=820 sum→
820=(40/2)(2*20.5)→
820=20*41
41
C
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Re: If n is the sum of the first 40 positive integers, what is the greates  [#permalink]

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New post 29 Oct 2018, 14:41
Smokeybear00 wrote:
If n is the sum of the first 40 positive integers, what is the greatest prime factor of n?

A. 29
B. 37
C. 41
D. 17
E. 19


Sum of first positive integers = x* (x+1)/2

Where x is the number of integers.

We are given number of positive integers = 40

so n would be 40 * 41/2

41 is the largest prime.

Answer choice C

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Re: If n is the sum of the first 40 positive integers, what is the greates  [#permalink]

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New post 29 Oct 2018, 16:46
Smokeybear00 wrote:
If n is the sum of the first 40 positive integers, what is the greatest prime factor of n?

A. 29
B. 37
C. 41
D. 17
E. 19


Sum = 40 × 41 / 2 = 820

Answer is simply the greatest prime factor of 820.

41
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Re: If n is the sum of the first 40 positive integers, what is the greates &nbs [#permalink] 29 Oct 2018, 16:46
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