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The difference is between factor pairs and distinct factors. With square numbers, one of the factor pairs will be the same number twice. When listing the distinct factors, that number is only listed once.
1,24
Pairs with common factors other than 1.
(20,1)(10,2)(5,4)
(1, 784); (2, 392); (4, 196); (7, 112); (8, 98); (14, 56); (16, 49); (28, 28)