What is the minimum number of letters that John has to send to be sure that Peter receives his letter

Question

John wants to send a letter to Peter, who lives on Tesla Street.
John doesn't remember the house number. However, he knows that it has 4 digits, it is a multiple of 5 and 7 and that the last digit is 0. What is the minimum number of letters that John has to send to be sure that Peter receives his letter?

Answer 1

so the last digit is zero which means it is a multiple of 10 and therefore is already divisible by 5
and also as it is a multiple of 7. So it is a multiple 70.
assuming the first digit can be zero we will start from 0070 as no house has a number 0000
the closest number under 10000 divisible by 70 is 9940

using term = a +(n-1)d
9940 = 70 +(n-1)70
9940/70 =1+ n-1
n = 142

so the answer is 142

Answer 2

so the last digit is zero which means it is a multiple of 10 and therefore is already divisible by 5
and also as it is a multiple of 7. So it is a multiple 70.
assuming the first digit cannot be zero we will start from 1050
the closest number under 10000 divisible by 70 is 9940

using term = a +(n-1)d
9940 = 1050 +(n-1)70
994 -105 = (n-1)*7
n-1 = 889/7
n = 128

so the answer is 128