Question
What is the minimum number of positive factors of a 6-digit number of the form abbabb, where a and b represent distinct natural numbers?
Answer: Option C
:
C
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C
A number of the form xyyxyy will be divisible by 7,11 and 13 (difference between triplets at odd and even places is zero).
Also 1001*xyy = xyyxyy (1001= 7*11*13). If we can get a prime number of the form xyy, we can reduce the number of factors.
122 is not a prime number. 233 is a prime number. xyyxyy = 233233 = 7*11*13*233, so the number of factors = 2*2*2*2 = 16. Hence, option (c) is the right answer.
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