Question

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

• A. 16
• B. 4
• C. 24
• D. 8

Answer 1

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'$\times$1001
'abcabc' = 'abc' $\times$ 7 $\times$ 11 $\times$ 13
Since 'abc' is prime we can write 'abcabc' as - $p^1\times 7^1\times {11}^1\times {13}^1$

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