alleryThe largest number that divides 245 and 1029, leaving remainders 5 and 5 respectively, is
A48
B8
C16
D32
Answer & Solution
Correct answer: C. 16
The number divides $245-5 = 240$ and $1029-5 = 1024$.
Required number $= \gcd(240, 1024)$.
$240 = 2^4\cdot3\cdot5$, $1024 = 2^{10}$, so $\gcd = 2^4 = 16$.
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