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Credit card number validation

to verify the validity of a credit card we're going to follow this four-step method the first step is to add up the first and third number in each group and I multiply that sum by two so the first thing we're going to do is add up the first and third number so the 4 and 0 the 1 and the 3 5 and the 7 and the 9 and the 1 so adding all that together 2 4 1 3 5 7 9 and 1 give us 30 so then we're going to take this 30 multiply it by 2 to get 60 sure the second step is to count up the number of digits in the first and third place of each group that are 5 or more so from the numbers that we just added I'm going to check off the ones that are 5 or more so it's five to seven and the nine so three is third step is now we're going to add up the second and fourth number in each group excuse for the zero and the zero two and four six and eight zero and zero here so adding that together two and four six six is 12 and eight is 20 okay the final step is to add everything together from steps 1 2 & 3 so I'm adding all those numbers together so the 16 so 3 and the 20 gives me 83 now if this is a valid credit card number this number should be divisible by 10 so if I had 83 and divided it by 10 I would get 8 times with a remainder of 3 so this is not divisible by 10 because you should get no remainder so this credit-card number is not valid if we wanted to make it valid I would need a number that's divisible by 10 so you have two options there you can either go down to 80 or up to 90 if I go down to 80 I would have to go down by 3 or if I want to go to 90 I'll have to go up by 7 so if you take a look at what's going on the only numbers that really could change or anything in the third step because you just simply added those together the number that should change is what's called a check digit which is the last digit and so that was a zero so if I wanted to get down to 80 I would just have to subtract 3 and I can't do that so if I want to get to 90 I would add 7 so to make it valid the new check digit would have to go from 7 or 0 up to 7 so then this 0 from the third step would become a 7 making the step number 4 into a 90 and that's divisible by 10