# Make a multiplication table for Z5 (this should read Z sub 5)

neela | High School Teacher | (Level 3) Valedictorian

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Z5 multiplication table.

The Z5 congruence class consists of the numbers 0,1,2,3,4.

So Multiplication any 2 numbers in z system is given below:

In Z5 system we represent numbers by the rule:

a*b =  remainder part of a*b/5 . This means the system has numbers 0, 1,2,3 or 4.

Example 4 E  Z5  and 3 E Z5.

Therefore 4*3 = 12 = remainder of 12/5 = 2.

Similarly 4*2 = 8 = Remainder of (8/5) = 3

Similarly 4*1 = 4 = 4 only as (remainder of (4/5) = 4.

Similarly 0*4 = 0 obvious by the abve reason.

Now we write table of multiplication under Z5 system:

(*  5 ) :      0        1         2          3         4

0     :     0        0         0          0         0

1     :     0         1        2          3         4

2     :     0         2        4          1         3

3     :     0         3        1          4         2

4     :     0         4        3          2         1.