Finish the multiplication table handout by figuring out the table for Z

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 |