Show that:

x ≡ 6(mod 9)
x ≡ 5(mod 7)
x ≡ 12(mod 10)

Has a unique solution modulo 630.

Step 1:

GCF(9,7) = 1
GCF(9,10) = 1
GCF (7,10) = 1

Step 2:

9 x 7 x 10
= 630

Step 3:

c1 = 630/9 = 70
c2 = 630 / 7 = 80
c3 = 630/10 = 63

But how exactly am I supposed to go about proving theres a unique solution modulo 630?