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

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Joined: 30 May 2017
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If n is the sum of the first 40 positive integers, what is the greates [#permalink]

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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
[Reveal] Spoiler: OA

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

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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

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

=(41)(40) / 2

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

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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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08 Jun 2017, 14:48
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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

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.
[Reveal] Spoiler:
C

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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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
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Re: If n is the sum of the first 40 positive integers, what is the greates   [#permalink] 31 Aug 2017, 05:39
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