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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.
