Ah, the fascinating world of greatest common factors! Finding the GCF can sometimes feel like searching for a needle in a haystack, but fear not, for I am here to show you the way!
In this case, we have the numbers 385 and 1365. Let's take a closer look at their prime factorizations.
385 = 5 x 7 x 11
1365 = 3 x 5 x 7 x 13
Now, it's time to determine which factors are found in both. We can see that both numbers have a factor of 5 and 7. So, the greatest common factor (or HCF) is 5 x 7 = 35.
And there you have it, my friend! The greatest common factor of 385 and 1365 is a delightful number called 35. It's like finding a shiny diamond in a pile of rocks. Keep up the fantastic factorizing!