# In the froup Z_12, find |a|, |b|, and |a+b| a=6, b=2

In the froup ${Z}_{12}$, find |a|, |b|, and |a+b|
a=6, b=2
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Consider the provided qustion,
If a $\in {Z}_{n}$ then $|a|=\frac{n}{gcd\left(a,n\right)}$
here given ${Z}_{12}$. So, n=12
Given a = 6, b = 2
So, a + b = 6 + 2 = 8
$|a|=|6|=\frac{12}{gcd\left(6,12\right)}=\frac{12}{6}=2$
$|b|=|2|=\frac{12}{gcd\left(2,12\right)}=\frac{12}{2}=6$
$|a+|=|8|=\frac{12}{gcd\left(8,12\right)}=\frac{12}{4}=3$