Question

Consider the following credit card numbers and tell me if they are valid or not. If a number is invalid, write the valid credit number by changing the “check” digit. Show your work for full marks.

a. 4634 5163 4122 7983

b. 5321 4142 6379 4771

c. How many valid (according to the Luhn check) 16-digit credit card numbers are there that start with these 14 digits 4444 4444 4444 44? Give one of the valid credit card numbers.

Answer 1

more To Check the validity of credit card number'. 1) Add digits of 1 and 3 positions of every group and double the sum. &) count the digits at 1 & 3 positions of every group if digits are 5 or than that. 3) Add up second (2) & 6th position digits at every place. 4) Now Add all these, if total sum is divisible by 10 card number is valida 9 To make valid to valid, Check the Check digit that is right most digit and make possible divisibility by adding Subtracting a) 46 34 51634122 7983 i) (4+3 +5+6+4+2+7+8 ) *2 (39) *2 78 ii) count if' 25'='4 111) (6+4 +1+3+1+2 +9+3) - 29 ix) add all 78 +4+29 EIU. 111% 10 = | not valrd Oy -

To make this valrd, change the check digil- Dearer to 10's modulo. i.e 4694 5163 4122 798 3 t Change to L 3-172 I as " is 111%10=1 So change with difference i valid credit card number =) so 4634 5163 4122 7982 16 5321 41426379 477) i) (5+2+4+4 +6 + 7 +4+7) *1 39 *2 = 78 a) count if 75 4 111) ( 3+1+1+2+3+9+ 7 +1) = 27 iu) -) 78 +4+27 109 109 7.10 - 9 Not valid tso change check digit by !/(add) to make it falid r. Valid a 5321414263794772 .)

c. According to LUHN Check, to find valid Credit card numbers that starts with +५५५ ५५५५ ५५५५ ५५ ** Valid numbers possible are 10" Ex's Valid credit card possible are ५५५५ ५५५५ ५५५५ ५५ 22

LUHN validity is done as 4 4 4 4 4 4 4 4 4444 44 22 15 14 13 12 1 10 9 8 7654 32 → Som of digits at odd places + (Sum of digits at even)* 2 %10-0. t Valid so (q +4+4+4+4+4+4+4) = 30 (2+4+4+4+4+4 +4+4)*3 = 30*2300 - Go +30 = 90 %10=0 (valid)

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