Question

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

Answer 1

Answer:

6

Step-by-step explanation:

$abc \: \times 2 = abcabc \\ 3 \times 2 = abcabc \\ 6 = abcabc$

Answer 2

Given data: 3 digit number 'abc' has 3 factors

To find: how many factors does the 6-digit number 'abcabc' have?

Solution:

abc has 3 factors and it is considered as a.

abcabc = $(a)^2$× 1001 ( square of prime number because it as 3 factors)

=> $a^2$ × 11 × 7 × 13

There are 2 possibility.

If a is different prime number other than 11, 13 and 7, The number of factors are 3 × 2 × 2 × 2 = 24.

If a is one of the prime number among 11, 13 and 7, The number of factors are  4 × 2 × 2 = 16.

Hence the number of factors are 16 or 24.