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Answer:
8
Step-by-step explanation:
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 64: 1, 2, 4, 8, 16, 32, 64
They share 1, 2, 4, and 8. 8 is the greatest digit in this case therefore it's your final answer.