how do we find the least residue of
1789 (mod 4), (mod 10), (mod 101)
Well, let's see... finding the least residue of a number modulo another number involves finding the remainder when we divide the original number by the modulo.
For 1789 (mod 4), we divide 1789 by 4 and get a remainder of 1. So the least residue is 1, which means that 1789 is congruent to 1 modulo 4.
Now, for 1789 (mod 10), we divide 1789 by 10 and again get a remainder of 9. So the least residue is 9, which means that 1789 is congruent to 9 modulo 10.
Lastly, for 1789 (mod 101), we divide 1789 by 101 and get a remainder of 86. So the least residue is 86, which means that 1789 is congruent to 86 modulo 101.
And there you have it! The least residues of 1789 modulo 4, 10, and 101 are 1, 9, and 86 respectively.
To find the least residue of a number modulo a divisor, we need to divide the number by the divisor and find the remainder. Let's find the least residues for each case:
1. 1789 (mod 4):
Dividing 1789 by 4 gives us a quotient of 447 and a remainder of 1. Therefore, the least residue of 1789 modulo 4 is 1.
2. 1789 (mod 10):
Dividing 1789 by 10 gives us a quotient of 178 and a remainder of 9. Therefore, the least residue of 1789 modulo 10 is 9.
3. 1789 (mod 101):
Dividing 1789 by 101 gives us a quotient of 17 and a remainder of 72. Therefore, the least residue of 1789 modulo 101 is 72.
To find the least residue of a number modulo another number, we need to find the remainder after dividing the number by the specified modulus.
1. Finding the least residue of 1789 (mod 4):
To find the least residue of 1789 modulo 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. Finding the least residue of 1789 (mod 10):
To find the least residue of 1789 modulo 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. Finding the least residue of 1789 (mod 101):
To find the least residue of 1789 modulo 101, divide 1789 by 101 and find the remainder.
1789 ÷ 101 = 17 remainder 72
Therefore, the least residue of 1789 (mod 101) is 72.