What is the greatest integer that will always evenly divide the sum of seven consecutive integers?  Choose the correct option:
A) 2  B) 3  C) 4  D) 7  E) 12
Let the three consecutive even integers be x , x + 7 , x+14 , x+21 , x+28 , x+35, x+42   Sum = x + x + 7 + x + 14 + x + 21 + x + 28 + x + 35 + x + 42   = 7x+147 = 7(x+21)   Therefore , 7 will always be a factor .   Answer 7
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What is the greatest integer that will always evenly divide the sum of seven consecutive integers?