Compilation - Number

Important Notes

Product of all the factors of any positive integer P equals P^F/2; Where F is the number of factors of P.


Fermat's Theorem:

a^(p-1)K divided by p is 1

Wilson Theorem

If P is prime number then (P-1)!-1 is divisible by P
Example usage


Remainder :-
Numerator 4 denominator 6 any power reminder is 4

Last 2 digits:-
-Number ending in 1 3 7 9 convert last digit to 1 and multiply 10th place with power for 2nd last digit.

-Number ending in 5.

Let me consider two cases where the numbers are ending with 5.
Numbers where the previous digit of 5 is 0 or any even number and
Numbers where the previous digit of 5 is any odd number

In 1st case if you raise the number to any power you'll always get 25 as the last two digits.
In 2nd case if you raise the number to even power you'll get 25, but in case of odd power you'll get 75 as the last two digits.

-Number ending with 2 4 6 8

24^n ends with 76, if n is even
24, if n is odd.
for 4 6 8 split the number into two. one having 2 and other having a odd number and use above method.



Types of questions

Finding remainder

method 1

Sample question
http://totalgadha.com/mod/forum/discuss.php?d=6454

a long dividend will be given. typically one in which pattern is bein ffollowed and addition of terms are easier.

convert number in form of ak1+r1 ,bk2+r2

where ab will be your divisor.

find value of the above equation.

solution number will be given by.

abk3+r3 where r3 is

the solution. try matching option with individual equation as well 

wrong option will not match even partially

Type2

formula based question.

find sum of factors.

find co primes using formula. the answer you get includes 1 in it.

Tips

In question where xy needs to me found out and you 2 equation, it is better to use option.

for eg if you have a number increased by 2 and reduced by 1. check the factors. quatient should have difference of one and factor shoul have diff of 2.

1001 is divisible by 11, 7 and 13 and is used to check simultaneous divisibility by 11, 7 and 13

Resource
Total Gadha
Last Two Digit