To find \(40 \times 9 \pmod{23}\), we first compute \(40 \mod 23\).
\[
40 \div 23 = 1.739
\]
The integer part of the division is 1, so we calculate the remainder:
\[
40 - 23 \times 1 = 40 - 23 = 17
\]
Thus,
\[
40 \equiv 17 \pmod{23}
\]
Next, we need to find \(17 \times 9 \pmod{23}\). First, calculate \(17 \times 9\):
\[
17 \times 9 = 153
\]
Next, we find \(153 \mod 23\):
\[
153 \div 23 = 6.652
\]
The integer part of the division is 6, so we calculate the remainder:
\[
153 - 23 \times 6 = 153 - 138 = 15
\]
Thus,
\[
153 \equiv 15 \pmod{23}
\]
Therefore, \(40 \times 9 \pmod{23}\) is:
\[
\boxed{15}
\]
Calculate $40*9 \pmod{23}.$ Express your answer as a non-negative integer that is less than $23$.
1 answer