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.
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Question 1098617: 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(52754) (Show Source):
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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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Let me re-formulate the problem in more precise (but still equivalent) terms.
A six-digit number is formed by repeating a three-digit number as in 639639.
Find the sum of the prime factors that are common for all such numbers.
Each number of the given form 639639 is the product of its "root" (in the sense "prefix" or "suffix" or "parent number") 639
and the number 1001.
It is clear that prime numbers that are common for all such numbers are those and only those that divide 1001.
Such prime numbers are 7, 11, and 13: 7*11*13 = 1001.
