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prathyushaR
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GMAT 1: 760 Q51 V41
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What is the smallest prime factor of 5^8+10^6–50^3? 22 Mar 2020, 02:28
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prathyushaR
the expression can be rewritten as:
\(5^8+(5^6 * 2^6)-(5^3 * 10^3) = 5^8 + (5^6 * 2^6)-(5^3*5^3*2^3) = 5^8 + (5^6 * 2^6)- (5^6 * 2^3)\)
which reduces to:
\(5^6(5^2+2^6-2^3)= 5^6(25+64-8)=5^6(81)=5^6 * 3^4\)
thus 3 is the smallest prime factor

The key here is :to reduce the expression in order to find its basic prime components only then can we decide which is the smallest prime factor
ANSWER: B


You can do it by Remainders also-

checking by 2 =
Remainder of 5^8 by 2 = 1
Remainder of 10^6 by 2 = 0
Remainder of 50^3 by 2 = 0

Thus By Remainder theorum : 1+0-0 = 1 NOT divisible by 2

Checking by 3-
Remainder of 5^8 by 3 = 1
Remainder of 10^6 by 3 = 1
Remainder of 50^3 by 3 = 2

Thus By Remainder theorum : 1+1-2 = 0 , hence the same is divisible by 3 , THUS CHOICE B
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Sure, but it takes a longer time for most to do such calculation. also if that's how you work better , by all means!
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What is the smallest prime factor of 5^8+10^6–50^3? 26 Mar 2025, 22:13
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