how do we find the least residue of
1789 (mod 4), (mod 10), (mod 101)
If I remember modular arithmetic
1789(mod4) = 1
1789(mod10) = 9
1789(mod101) = 72
I don't know what you mean by "least residue"
To find the least residue of a number, say 1789, modulo a given modulus, such as 4, 10, and 101, we need to compute the remainder when 1789 is divided by each modulus. Let's compute the least residues for each case:
1. Modulo 4:
To find the least residue of 1789 (mod 4), we divide 1789 by 4 and find the remainder. In this case, 1789 divided by 4 is 447 remainder 1. Therefore, the least residue of 1789 (mod 4) is 1.
2. Modulo 10:
To find the least residue of 1789 (mod 10), we divide 1789 by 10 and find the remainder. In this case, 1789 divided by 10 is 178 remainder 9. Therefore, the least residue of 1789 (mod 10) is 9.
3. Modulo 101:
To find the least residue of 1789 (mod 101), we divide 1789 by 101 and find the remainder. In this case, 1789 divided by 101 is 17 remainder 72. Therefore, the least residue of 1789 (mod 101) is 72.
In summary, the least residues for 1789 (mod 4), (mod 10), and (mod 101) are 1, 9, and 72, respectively.