Arithmetic1

square of a number: n^2=(n+1)^2-(n+1)-n                  square of a number =square of a after number-(after number)-(number)                        example=9^2=10^2-10-9                                             =100-10-9                                             =100-19                                             =81                                       19^2=20^2-20-19                         ...

procedure to find the factors of  48: when you want to start calculating the factors start from 1. 1 is a common factor for all numbers. the following table shows the factors of 48                                          1 X 48 = 48 2 X 24 = 48 3 X 16 = 48 4 X 12 = 48 6 X 8 = 48 8 X 6 = 48 12 X 4 = 48 16 X 3 = 48 24 X 2 = 48 48 X 1 = 48 as shown in the above table  in first row multiply 1 by  number 48. from second row try for all possible  numbers so that their multiplication gives 48. then the first column shows the factors of number 48 which are shown in...

The prime numbers from 1 to 1000 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 By seeing above the table of prime numbers from 1 to 1000 we can observe that 168 prime numbers are there. by seeing the below table we can observe how the prime numbers are distributed. 1-100 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97 25 101-200 101, 10...

In all competitive exams questions on prime numbers are asked. Prime numbers are important when you are concerned series questions. Now we will see how to write prime numbers. Multiple of 2: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100 Multiple of 3:3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99 Multiple of 4: 4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100 Multiple of 5: 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100 Multiple of 6: 6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96 Multiple of 7: 7,14,21,28,35,42,49,56,63,70,77,84,91,98 Multiple of 8: 8,16,24,32,40,48,56,64,72,80,88,94 Multiple of 9:9,18,27,36,45,54,63,72,81,90,99 Multiple of 10: 10,20,30,40,50,60,70,80,90,100 Multiple of 11: 11,22,33,44,55,66,77,88,99 Now WE will write the number from 1 to 100 e ...

The natural numbers are 1,2,3,4,5,. . . . . . now we will see the sum of natural numbers                       sum of first 3 natural numbers= 1+2+3=6 the above can be written as                      sum of first 3 natural numbers= 1+2+3=6=3(3+1)/2                      sum of first 4 natural numbers= 1+2+3+4=4(4+1)/2                      then sum of n natural numbers=1+2+3+......n terms=n(n+1)/2 then the average formula = sum of elements/no of elements                     the average of n natural numbers= sum of elements/ no of elements                                                ...

Even numbers are 2,4,6,8,10,…. Average = sum of elements/ no of elments Now we will see the sum of elements: Sum of first 2 even numbers: 2+4= 6= 2(2+1) Sum of first 3 even numbers: 2+4+6= 12= 3(3+1) Sum of first 4 even  numbers: 2+4+6+8=20= 4(4+1) Sum of first 5 even numbers: 2+4+6+8+10 = 30 = 5(5+1) Sum of first n even numbers: 2+4+6+8+10+. . . . .  n numbers= n(n+1) Now we will see average: Average of first 2 even numbers= (2+4)/2                                                           = 6/2                              ...

Procedure to find the factors of  88: when you want to start calculating the factors start from 1. 1 is a common  factor for all numbers. the following table shows the factors of 88 1 X 88 = 88 2 X 44 = 88 4 X 22 = 88 8 X  11 = 88 11 X 8 = 88 22 X 4 = 88 44 X 2 = 88 88 X 1 = 88            as shown in the above table  in first row multiply 1 by   number 88. from second row try for all possible numbers so that their multiplication gives 88. then the first column shows the factors of number 88 which are shown in red colour:   factors of number 24 are :  1, 2, 4.8,11,22,44,88 if you divide the 88 with any one of the above factors reminder is zero

In a magic square 3x3, if we take numbers from 1 to 9 then the magic sum equal to 15. The magic square is as follows: 4 9 2  3 5 7 8 1 6 In the above magic square 3x3 magic sum is 15. In the above magic square 3x3 we are used numbers from1 to 9 arranged in 9 boxes. In any direction the sum equal to 15. Row wise  4+9+2=15, 3+5+7=15, 8+1+6=15. Column wise 4+3+8=15, 9+5+1=15, 2+7+6=15. Diagnol wise: 4+5+6=15, 2+5+8=15. The above magic square also can be written as follows: 5-1 5+4 5-3  5-2 5 5+2 5+3 5-4 5+1 In the above figure , shows the relation between middle number and other numbers. In the magic square we are taken numbers from 1 to 9 and number 5 is between 1 to 9. If we write  x in place of 5 in above magic square.                     ...