SOLUTION: A six-digit number is formed by repeating a three-digit number as in 639639. Find the sum of the prime factors all such numbers have in common.

Question 1186270: A six-digit number is formed by repeating a three-digit number as in 639639. Find the sum of the prime factors all such numbers have in common.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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A six-digit number is formed by repeating a three-digit number as in 639639.
Find the sum of the prime factors all such numbers have in common.
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All these six-digit numbers, described in the post, are of the form

      N = 1000n + n = 1001n,

where n is a/(any) three digit number.


Therefore, all such 6-digit numbers have common factor  1001.


Its prime decomposition is 1001 = 7*11*13.


Its positive prime factors are  7, 11, 13.


The sum of these factors is 7 + 11 + 13 = 31.


ANSWER.  31.

Solved.

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