If a three digit number lsquo abc rsquo has 2 factors where a b c are digits how many factors does t...........

Quant (SSC) Number System

If a three digit number ‘abc’ has 2 factors (where a, b, c are digits), how many factors does the 6-digit number ‘abcabc’ have?

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Explanation:

To start with ‘abcabc’ = ‘abc’ * 1001 or abc * 7 * 11 * 13
‘abc’ has only two factors. Or, ‘abc’ has to be prime.
Only a prime number can have exactly two factors.
So, ‘abcabc’ is a number like 101101 or 103103.
’abcabc’ can be broken as ‘abc’ * 7 * 11 * 13. Or, a p * 7 * 11 * 13 where p is a prime.
As we have already seen, any number of the form p^aq^br^c will have (a + 1) (b + 1) (c + 1) factors, where p, q, r are prime.
So, p * 7 * 11 * 13 will have = (1 + 1) * (1 + 1) * (1 + 1) * (1 + 1) = 16 factors