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To find the greatest common factor of two numbers, you first need to break those numbers down into their prime factors. For 105 and 147 this is:
105 = 3x5x7
147 = 3x7x7
The next step is to identify any common prime factors. In this case, both numbers have a 3 as a prime factor, and a 7 as a prime factor. Multiply these together to get the GCF:
3x7 = 21
Thus the greatest common factor of 105 and 147 is 21.
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