No difference. In this context, highest and greatest mean the same thing.
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Since the product of two numbers is equal to the product of their GCF and LCM, the GCF of two numbers is equal to their product divided by their LCM and their LCM is equal to their product divided by their GCF.
The HCF/GCF of 506 and 1863 is 23.
The GCF is 13.
The GCF is 1.
The GCF is 1.