Find the least residue of 260 mod 7 How can you find the lea

Find the least residue of 260 (mod 7). How can you find the least residue of any positive integer (mod 100) by inspection? For example what is the least residue of 54893874657849382734748594878578904098745 (mod 100).

Solution

a)260=7*37 +1

so 1 is the least residue of 260 (mod 7)

b) least residue of any positive integer (mod 100)

whenever we divide any positive integer by 100 we get the last two digits of that number asreminder

for example 143 (mod 100)=43

so 54893874657849382734748594878578904098745 (mod 100)= 45