Group Elements of Z24: Find the Order

[Yara Leonard]

Determine the order of every element of Z24

 

[kaliprasad]

kindly infrom what you have tried and where you are facing problems

 

[HOI]

Do you understand that "z24" is the additive group of integers modulo 24? That has 23 non-zero members so you will need to give 23 answers. Do you further understand that the "order" of a member, a, of a group is the integer "n" such that na= 0 where "na" means a added to itself n times. For example 6+ 6+ 6+ 6= 24= 0 (mod 24) so 6 has order 4. No multiple of 5 will be 24 so the order of 5 (and any number that is not a divisor of 24) is "infinity".