CYCLICITY

CYCLICITY
 This concept is mainly about the unit digit of a number and its repetitive pattern on being divided by a certain number.
The concept of cyclicity can be learned by fighring out the unit digits of all the single digit numbers from 0 - 9 when raised to certain powers.
Digits 0, 1, 5 & 6: When we observe the behaviour of these digits, they all have the same unit’s digit as the number itself when raised to any power, i.e., .\({0^n} = 0,{1^n} = 1,{5^n} = 5,{6^n} = 6\) Let’s apply this concept to the following example.
Example : Find the unit’s digit of following numbers :
    \({185^{563}}\) = 5
   \({271^{6987}}\) = 1
     \({156^{25369}}\)= 6
   \({190^{654789321}}\) = 0
The number in the form 5ⁿ,n\(\in z\)
            
Example : The unit’s place digit in the expansion of 5⁹⁹⁹ is 5.
The number in the form of 6ⁿ,\(n\in z\)

Example : The unit’s place digit in the expansion of 6²⁰⁰⁸ is 6.