Let p be a prime number greater than 2 and let N = 14p. How many even numbers divide N?
Options:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5 Stream of consciousness first, then make a decision:
Answer: A. There is exactly one. The prime factorization of 14 is 14 = 2*7, so N = 2*7*p = 7*2*p = 7*2p, so 2p is the only even number that divides N.
Thus, the answer is (A).