Looking for patterns in the multiplication table mod n:

Finish the multiplication table handout by figuring out the table for Z₅ and Z₆

A unit is a number that has a multiplicative inverse,  You can find units by looking in the multiplication table to see if there is a 1 in the row.  If there is, that number is a unit.  Color/circle/highlight each unit in red or orange or yellow or pink.

A zero divisor is either of a pair of  numbers such that ab=0, but neither factor=0.  For example, 2 and 3 are not 0 in mod 6, but (2)(3)=0(mod 6). Color/circle/highlight each zero divisor in blue, green or purple.

Example:

x mod 6	0	1	2	3	4	5
0	0	0	0	0	0	0	not a zero divisor because zero doesn't count as a zero divisor
1	0	1	2	3	4	5	1 is a unit because 1*1=1
2	0	2	4	0	2	4	2 is a zero divisor because 2*3=0 (and 2,3 both not zero)
3	0	3	0	3	0	3	3 is a zero divisor because 3*2=0 and 3*4=0
4	0	4	2	0	4	2	4 is a zero divisor because 4*3=0
5	0	5	4	3	2	1	5 is a unit because 5*5=1