For each m with 6 ≤ m ≤ 13, how many zero divisors does Z/mZ have?

An element, [a] will either be a unit or a zero divisor, so check to see if (a,m)=1. If so then, this is a unit and not a zero divisor. If 1< gcd(a,m)<m, then [a] is a zero divisor. For example Z/12Z has 7 zero divisors:

(1,12) is not because (1,12)=1 making it a unit

(2,12) has a gcd less than 12 and therefore satisfies 1<(2,12)<m, so it's a zero divisor

(3,12) zero divisor

(4,12) zero divisor

(5,12)=1 so not a zero divisor

(6,12) zero divisor

(7,12) not zero divisor

(8,12) zero divisor

(9,12) zero divisor

(10,12) zero divisor

(11,12)not zero divisor

(12,12) not zero divisor

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