Number System Tutorials & Tricks
Introduction
A number is a mathematical object used to count, label, and measure. In mathematics, the definition of number has been extended over the years to include such numbers as 0, negative numbers, rational numbers, irrational numbers, real numbers, and complex numbers.
Formula for finding out Number System
1. Prime number: If number a divided another number b exactly, we say that a is a factor of b. A number which is not divisible by other numbers except the number itself and 1 is termed as prime number
2. Whole Number:Natural numbers with 0 are termed as whole number
3. Important Rules on Counting:-
Rule 1: Sum of first n natural numbers : = n(n+1)/2
Rule 2: Sum of first n odd numbers : = n*n/n2
Rule 3: Sum of first n even numbers = n(n+1)
Rule 4: Sum of squares of first n natural numbers : = n(n+1)(2n+1)/6
Rule 5: Sum of cubes of first n natural numbers : = [n(n+1)/2]2
Rule 6: If n is the number of numbers and n is even then n/2 numbers will be even and n/2 numbers will be odd among first n natural numbers.
Rule 7: If n is odd , then there are (n+1)/2 odd numbers and (n-1)/2 even numbers
Rule 8: The difference between the squares of two consecutive numbers is always an odd number. Eg. 92 - 82 = 17
Rule 9: The difference between the squares of two consecutive numbers is the sum of the two consecutive numbers
Rule 10: Dividend = (Divisor * Quotient) + Remainder
Rule 11: Sum of first n even numbers = n(n+1)
Sample Example
Ex
Find out the number of all even numbers from 1 to 300 ?
A
Since 300 is an even number so total number of even numbers wil be (n/20) = (300/2) = 150 even numbers/
Ex
What is the sum of all the even numbers from 1 to 381
A
Even numbers will be = (381-1)/2= 190 Sum of even numbers = n * (n+1) = 190 (190+1) = 36,290
Ex
Find out of sum of all the odd numbers from 50 to 200?
A
Required Sum = Sum of all odd numbers from 1 to 200 - Sum of all odd numbers from 1 to 50 : = 1002 - 252 = 9375
Ex
What least number must be added to 7963 to make it exactly divisible by 65 ?
A
On dividing 7963 by 65 we get 33 as remainder, So the number to be added will be 65 - 33 = 32
Ex
What least number must be subtracted from 7963 to make it exactely divisible by 65 ?
A
On dividing 7963 by 65 we get 33 as remainder, So the number to be subtracted will be 33
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