how do we find the least residue of

1789 (mod 4), (mod 10), (mod 101)

To find the least residue, we can use the modulus operator or the remainder when dividing.

1. Modulo 4:
To find the least residue of 1789 (mod 4), divide 1789 by 4 and find the remainder.
1789 ÷ 4 = 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), divide 1789 by 10 and find the remainder.
1789 ÷ 10 = 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), divide 1789 by 101 and find the remainder.
1789 ÷ 101 = 17 remainder 72
Therefore, the least residue of 1789 (mod 101) is 72.

To find the least residue of a number with respect to a modulus, we need to divide the number by the modulus and find the remainder. The remainder will be the least residue.

1) Least residue of 1789 (mod 4):
To find the least residue of 1789 (mod 4), we divide 1789 by 4 and find the remainder.
1789 ÷ 4 = 447 remainder 1
Therefore, the least residue of 1789 (mod 4) is 1.

2) Least residue of 1789 (mod 10):
To find the least residue of 1789 (mod 10), we divide 1789 by 10 and find the remainder.
1789 ÷ 10 = 178 remainder 9
Therefore, the least residue of 1789 (mod 10) is 9.

3) Least residue of 1789 (mod 101):
To find the least residue of 1789 (mod 101), we divide 1789 by 101 and find the remainder.
1789 ÷ 101 = 17 remainder 92
Therefore, the least residue of 1789 (mod 101) is 92.

I think I understand your question.

The mod(x,z) function says divide x by z and give the remainder. (does remainder mean "residue" in your question?)
So, mod(1789,4) is 447 and 1 remainder.
mod(1789,10) is 178 and 9 remainder.
mod(1789,101) is 17 and 72 remainder.