A quick test for 7 says: chop off the last digit, double it, and subtract it from what is left; repeat until you can judge the result by eye. Which of these numbers passes the test?

Apply the test to 3927: $392-2\times 7=392-14=378$, then $37-2\times 8=37-16=21$, and $21=7\times 3$. So $3927=7\times 561$. The others fail: 4321 reduces to 43 (remainder 1 on division by 7), 5683 leaves 6 and 2468 leaves 4. Note the test subtracts twice the last digit — subtracting the digit itself is the usual mistake and would wrongly pass 4321.