Answer
1
Work Step by Step
Use the Euclidean algorithm, we have:
1. Let $a:=1177, b:=509, r:=509$
2. as $b\ne0$, we have $r:=a\ mod\ b=1177\ mod\ 5095=159$
3. set $a:=509, b:=159$
4. as $b\ne0$, we have $r:=a\ mod\ b=509\ mod\ 159=32$
5. set $a:=159, b:=32$
6. as $b\ne0$, we have $r:=a\ mod\ b=159\ mod\ 32=31$
7. set $a:=32, b:=31$
8. as $b\ne0$, we have $r:=a\ mod\ b=32\ mod\ 31=1$
9. set $a:=31, b:=1$
10. as $b\ne0$, we have $r:=a\ mod\ b=31\ mod\ 1=0$
11. set $a:=1, b:=0$
12. output: gcd=1
