What is the gcf of 33 and 46?

We can use the Euclidean algorithm to find out:

46 = 1*33 + 13

33 = 2*13 + 7

13 = 1*7 + 6

7 = 1*6 + 1

The last remainder is 1, which means 33 and 46 are coprime and gcf (33, 46) = 1.

Another way to see this is to write out the prime factorizations of both numbers:

33 = 3*11

46 = 2*23

As you can see, there are no shared divisors, so the gcf is 1.