Rule for Divisibility by 8 A number with at least 3 digits is divisible by 8 if its last three digits form a number divisible by 8. Examples A.) 7,120 is divisible by 8 because its last three digits, 120, form a number divisible by eight. B.) 9,389 is not divisible by 8 because its last three digits, 389, form a number not divisible by eight. Proof For any integer x written as anan-1an-2...a2a1a0, we will show that x is divisible by 8 if a2a1a0 is divisible by 8. If we write x as anan-1an-2...a2a1a0, then we can also write: x=
a0 +
a1(10)
+ a2(102 )+
a3(103)...
+ an-2(10n-2)
+
an-1(10n-1
)
+
an(10n) =
(an×10n
+
an-1×10n-1
+
an-2×10n-2
+
.... + a3)×1000
+
a2a1a0 = 8×125× (an×10n + an-1×10n-1 + an-2×10n-2 + .... + a3) + a2a1a0 |