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The greatest common factor of 123 and 234 is 3.

123: the digits (1, 2, 3) add up to 6.

234: the digits (2, 3, 4) add up to 9.

So both 6 and 9 are divisible by three.

More formally:

The prime factors of 123 are 3 and 41, while the prime factors of 234 are 2, 3, 3, and 13. The intersection of [3, 41] and [2, 3, 3, 13] is [3], therefore the Greatest Common Factor (GCF) of 123 and 234 is 3.

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