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# What is the greatest prime factor of 1+2+3+….+36?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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What is the greatest prime factor of 1+2+3+….+36?  [#permalink]

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08 Oct 2018, 01:53
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15% (low)

Question Stats:

78% (00:50) correct 22% (01:06) wrong based on 68 sessions

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[Math Revolution GMAT math practice question]

What is the greatest prime factor of $$1+2+3+….+36$$?

$$A. 2$$
$$B. 3$$
$$C. 9$$
$$D. 31$$
$$E. 37$$

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" NUS School Moderator Joined: 18 Jul 2018 Posts: 1019 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) Re: What is the greatest prime factor of 1+2+3+….+36? [#permalink] ### Show Tags 08 Oct 2018, 02:15 Sum = n(n+1)/2. Sum = 36(37)/2 = 18*37. Prime factoring gives 3^2*2*37. Greatest prime factor = 37. E is the answer Posted from my mobile device _________________ Press +1 Kudos If my post helps! Director Joined: 20 Feb 2015 Posts: 762 Concentration: Strategy, General Management Re: What is the greatest prime factor of 1+2+3+….+36? [#permalink] ### Show Tags 08 Oct 2018, 04:27 MathRevolution wrote: [Math Revolution GMAT math practice question] What is the greatest prime factor of $$1+2+3+….+36$$? $$A. 2$$ $$B. 3$$ $$C. 9$$ $$D. 31$$ $$E. 37$$ sum can be written as 36*37/2 = 37 * 18 greatest prime factor = 37 E VP Joined: 31 Oct 2013 Posts: 1464 Concentration: Accounting, Finance GPA: 3.68 WE: Analyst (Accounting) Re: What is the greatest prime factor of 1+2+3+….+36? [#permalink] ### Show Tags 08 Oct 2018, 05:16 1 MathRevolution wrote: [Math Revolution GMAT math practice question] What is the greatest prime factor of $$1+2+3+….+36$$? $$A. 2$$ $$B. 3$$ $$C. 9$$ $$D. 31$$ $$E. 37$$ The challenge is that how we can determine the sum of this serious. we can do it by applying the following formula. 36 + 1 = 37 35 + 2 = 37 at the same way we can make such pair. we will have 18 pairs as total we have is 36 integers. 37*18 = total. NO need to multiply. *** 37 is a prime. So it's the greatest prime. The best answer is E. GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 935 What is the greatest prime factor of 1+2+3+….+36? [#permalink] ### Show Tags 08 Oct 2018, 05:50 MathRevolution wrote: [Math Revolution GMAT math practice question] What is the greatest prime factor of $$1+2+3+….+36$$? $$A. 2$$ $$B. 3$$ $$C. 9$$ $$D. 31$$ $$E. 37$$ $$?\,\,\,:\,\,\,{\rm{greatest}}\,\,{\rm{prime}}\,\,{\rm{factor}}$$ $$1 + 2 + 3 + \ldots + 36\,\,\mathop = \limits^{\left( * \right)} \,\,\left( {{{1 + 36} \over 2}} \right) \cdot 36 = 18 \cdot 37\,\,\,\,\mathop \Rightarrow \limits^{2,3\,\,{\rm{or}}\,\,37} \,\,\,\,? = 37$$ (*) 1, 2, 3, ..., 36 is a finite arithmetic sequence, hence their average is equal to the average of the first and last terms (or any two symmetric to the median). Besides that, the sum 1+2+3+...+36 is equal to the average (explained above) times the number of parcels (36), due to the homogeneity nature of the average. This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net GMAT Club Legend Joined: 12 Sep 2015 Posts: 4007 Location: Canada Re: What is the greatest prime factor of 1+2+3+….+36? [#permalink] ### Show Tags 08 Oct 2018, 06:37 Top Contributor MathRevolution wrote: [Math Revolution GMAT math practice question] What is the greatest prime factor of $$1+2+3+….+36$$? $$A. 2$$ $$B. 3$$ $$C. 9$$ $$D. 31$$ $$E. 37$$ Useful formula: 1 + 2 + 3 + 4 + . . . . + n = (n)(n + 1)/2 So, 1 + 2 + 3 + …. + 36 = (36)(36 + 1)/2 = (36)(37)/2 = (18)(37) = (2)(3)(3)(17) So, the greatest prime factor is 37 Answer: E Cheers, Brent _________________ Test confidently with gmatprepnow.com Manager Joined: 24 Dec 2017 Posts: 185 Location: India Concentration: Strategy, Real Estate Schools: Johnson '21 Re: What is the greatest prime factor of 1+2+3+….+36? [#permalink] ### Show Tags 08 Oct 2018, 07:07 Formula: 1st term + Last term/2 x number of terms in the series Let's apply it =>(1+36)/2 x 36 =>37 x 18 = 666 From the above, we can arrive at the answer. Greatest prime factor is 37 (E) Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8017 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the greatest prime factor of 1+2+3+….+36? [#permalink] ### Show Tags 10 Oct 2018, 00:59 => Since $$1 + 2 + 3 + … + n = \frac{n(n+1)}{2}$$, we have $$1 + 2 + 3 + … + 36 = \frac{(36*37)}{2} = 18*37 = 2*32*37.$$ Thus, $$37$$ is the greatest prime factor of $$2*3^2*37.$$ Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: What is the greatest prime factor of 1+2+3+….+36?   [#permalink] 10 Oct 2018, 00:59
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