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