hcf of two no. : GMAT Quantitative Section
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# hcf of two no.

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18 Dec 2012, 18:37
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If A = (2^(20) -1) and B = (2^(110) - 1). Then HCF(A,B) =
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18 Dec 2012, 19:29
Hii welcome to GMATCLUB.
Please see the rules before posting.

In this question, the answer must be 3.
Take two numbers for easy calculation: 2^6 and 2^8.
So 2^6 - 1=63, 2^8 - 1=255.
Hcf is 3.
Hence IMO for the two numbers in question, the hcf will be 3.
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18 Dec 2012, 23:27
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juantheron wrote:
If A = (2^(20) -1) and B = (2^(110) - 1). Then HCF(A,B) =

Use a^2 - b^2 = (a + b)(a - b) to factorize the expressions.

$$A = 2^{20} - 1^{20} = 2^{10*2} - 1^{10*2} = (2^{10})^2 - (1^{10})^2 = (2^{10} + 1^{10})(2^{10} - 1^{10})$$
$$B = 2^{110} - 1^{110} = 2^{10*11} - 1^{10*11} = (2^{10})^{11} - (1^{10})^{11} = (2^{10} - 1^{10})(2^{100} + ....)$$

(Difference of odd powers is divisible by the difference of the numbers e.g. x^3 - y^3 is divisible by x-y)

The highest common factor must be$$(2^{10} - 1^{10}) = 2^{10} - 1$$
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews VP Status: Been a long time guys... Joined: 03 Feb 2011 Posts: 1420 Location: United States (NY) Concentration: Finance, Marketing GPA: 3.75 Followers: 175 Kudos [?]: 1334 [0], given: 62 Re: hcf of two no. [#permalink] ### Show Tags 19 Dec 2012, 01:57 Hi Karishma. Is there any alternate way to do this question? I tried picking up a smaller number but failed as evitable by your explanation. _________________ Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7119 Location: Pune, India Followers: 2131 Kudos [?]: 13631 [0], given: 222 Re: hcf of two no. [#permalink] ### Show Tags 19 Dec 2012, 20:02 Marcab wrote: Hi Karishma. Is there any alternate way to do this question? I tried picking up a smaller number but failed as evitable by your explanation. There is no reason that the HCF of two small numbers will be the same as the HCF of two larger numbers. The question is meant to test your application of algebraic identities. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: hcf of two no.   [#permalink] 19 Dec 2012, 20:02
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