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23 Sep 2020, 05:18
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
90% (00:47) correct
10%
(01:18)
wrong
based on 73
sessions
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What is the greatest prime number that is a divisor of both 380 and 570?
A. 5
B. 7
C. 11
D. 17
E. 19
A. 5
B. 7
C. 11
D. 17
E. 19
23 Sep 2020, 05:33
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Prime factorising 380 - 2^2*5*19
check if 570 is divisible by 19 - yes. Answer 19.
check if 570 is divisible by 19 - yes. Answer 19.
23 Sep 2020, 09:37
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The prime factorizations are so simple here that I'd do this exactly how vijk did above. If it wasn't immediately obvious how to prime factorize (say the numbers instead were 399 and 589), you could take advantage of this: if x and y are both divisible by some number d, then x+y and x-y will always be divisible by d too. So here, we're looking for a prime that divides 570 and 380, and that prime will automatically also divide 570 - 380= 190. So now we can think about a smaller number than either of the numbers in the question, which is advantageous if the numbers in the question are awkward. The only primes that divide 190 are 2, 5 and 19, so one of those must be the answer (we still need to check that 19 'works' to finish the question though, since x-y can also be divisible by 19 when neither x nor y is divisible by 19, e.g. with x=39 and y=20).
