Determine the gcd of the following integers:
(a) −12, 34
(b) −36, −60
(c) 60, −72
(d) 1001, 182
We only need to consider positive integers, so can ignore negative factors.
(a) The factors of -12 are $\{1, 2, 3, 4, 6, 12\}$. The factors of 34 are $\{1, 2, 17, 34\}$.
The gcd is therefore 2.
(b) The factors of -36 are $\{1, 2, 3, 4, 6, 9, 12, 18, 36\}$. The factors of -60 are $\{1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60\}$.
The gcd is therefore 12.
(c) The factors of 60 are $\{1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60\}$. The factors of -72 are $\{1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72\}$.
The gcd is therefore 12.
(d) The factors of 1001 are $\{1, 7, 11, 13, 77, 91, 143, 1001\}$. The factors of 182 are $\{1, 2, 7, 13, 14, 26, 91, 182\}$.
The gcd is therefore 91.