Question

the order of the element (4,2) in Z12 × Z8​

Answer 1

Answer: The order of (4,2) in Z12 x Z8 = 12

Step-by-step explanation:

In order to find the order of an element (a,b) in Zm x Zn, the following steps must be followed:

• HCF of (a,m)
• Divide 'm' by the HCF of (a,m)
• HCF of (b,n)
• Divide 'n' by the HCF of (b,n)
• Find the LCM of the numbers obtained by dividing 'm' and 'n'.

In the given question, to find the order of (4,2) in Z12 x Z8, we follow the aforementioned steps:

• HCF of (4,12) = 4.
• $\frac{12}{4} =<strong>3$
• HCF of (2,8) = 2.
• $\frac{8}{2} = <strong>4$
• LCM of (3,4) = 12.

Thus, the order of (4,2) in Z12 x Z8 = 12.