If a 3 digit number 'abc' has 3 factors, how many factors does the 6-digit number 'abcabc' have?

Options:

A . 16 factors

B . 24 factors

C . 16 or 24 factors

D . 20 factors

E . 5.12 am

Answer: Option C : C 'abc' has exactly 3 factors, so 'abc' should be square of prime number. Let the square root of 'abc' be 'p' (where 'p' is prime). 'abcabc'= abc× 1001 = p2×13×11×7 If 'p' is any prime number other than 13, 11 or 7, then no. of factors = 3 x 2 x 2 x 2 = 24 (no. will be of the formp2×13×11×7) If 'p' is any prime number among 13, 11 or 7, then no. of factors = 4 x 2 x 2 = 16 (no. will be of the form73×13×11,ifp=7) ∴ No. of factors can be 16 or 24.

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