Primefactors

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lucas211: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Mon Aug 04, 2014 5:39 pmFollowed by: 2 members; Thanked: 1 times

by lucas211 » Wed Feb 17, 2016 5:01 am

Hello everybody

Would appreciate a little help on this question:

What is the smallest prime factor of 5^8+10^6-50^3 ?

a) 2
b) 3
c) 5
d) 7
e) 11

Thanks in advance

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Source: Beat The GMAT — Problem Solving | Wed Feb 17, 2016 5:01 am

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Wed Feb 17, 2016 6:24 am

lucas211 wrote:Hello everybody

Would appreciate a little help on this question:

What is the smallest prime factor of 5^8+10^6-50^3 ?

a) 2
b) 3
c) 5
d) 7
e) 11

Thanks in advance

First factor the equation into powers of 5 and 2

5^8 + (2^6)(5^6) - (5^6)(2^3)

Bring out the 5^6

5^6*(5^2 + 2^6 - 2^3)

Simplify inside the brackets

5^6*(25 + 64 - 8) =

5^6*(81) = 5^6*(3^4)

Smallest prime factor is therefore 3

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