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# Number System Questions and Answers

# Number System Questions

## Definition of Number System

**Number System is used in nearly every single subject matter in maths. It to a great extent describes the significance of this subject. Number System mostly involves additional sub-topics such as HCF & LCM, factors, factorials, cyclicity, Euler number, digital root, unit digit, and more. The conception of unit digit can be well-read by assuming out the unit digits of all the sole digits ranging from 0 – 9 when elevated to definite capacities. The numbers are widely categorized into three groups for this use.**

**Rules**

- One of the key things to note while solving questions related to number systems is that the difference between the square of two consecutive values is the total of the two consecutive numbers.
- The result is always an odd number if the squares of two consecutive numbers are subtracted.
- If there is an even number in the unit place of the value given, then afterwards the times it is multiplied, it will still have the similar number in the unit place, which is:

(…..1)n=(…1)

(…7)n=(….7)

(……4)n=(……..4) - If there is an odd number at the unit place (excluding 5), multiply the value by the same until it reaches to 1 in the unit place:

(……….1)n= (……….1)

(…..3)4n = (……1)

(…….7)4n = (…….1)

Where n = 1, 2, 3