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Question

If a 3-digit number 'abc' has 2 factors, how many factors does the 6-digit number 'abcabc' have?

A

16

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B

4

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C

24

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D

8

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Solution

The correct option is A

16


'abc' has 2 factors.
This means 'abc' is a prime number (Only a prime number can have exactly 2 factors).
Now, 'abcabc' = 'abc'×1001
'abcabc' = 'abc' × 7 × 11 × 13
Since 'abc' is prime we can write 'abcabc' as - p1×71×111×131

No. of factors = (1+1) (1+1) (1+1) (1+1) = 16 factors.

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