The number 503 is a prime number. How many positive integers are factors of 2012 ?
(A) 2
(B) 3
(C) 7
(D) 6
(E) 8
Both 1 and 2012 are obvious positive integer factors of 2012.

Since 2012 is an even number and $2012 \div 2=1006$, then both 2 and 1006 are factors of 2012 . Since 1006 is also even then 2012 is divisible by 4 .

Since $2012 \div 4=503$, then both 4 and 503 are factors of 2012 .

We are given that 503 is a prime number; thus there are no additional factors of 503 and hence there are no additional factors of 2012.

The factors of 2012 are 1 and 2012, 2 and 1006, 4 and 503.

Therefore, there are 6 positive integers that are factors of 2012.

ANSWER: (D)

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