Divisibility rules are shorthand ways of division to tell if one number is divisible or not. Here is a proof the divisibility rule of number 61 with simple example. You can check if a number is divisibile by 61 using the rule given here.
Multiply 6 times the last digit of the given number and subtract it from the rest of the digits. (i.e.,) if ABCD is the given number, subtract 6 times of D from ABC. If the resultant number is divisble by 61, then the given number is also divisible by 61. Apply this rule over and over again as necessary.
Check if 732 is Divisible by 61
Apply the divisibility rule of number 61 and check if 732 is divisible by 61.
The last digit of the given number is 2. 6 times of the last digit is (6 x 2 = 12)
Subtract the resultant number from the other given digits. 73 - 12 = 61
Since 61 is divisible by 61, the original number 732 is also divisible by 61.