Divisibility cont. #
Example
Find a number with the amount of divisors of
\( N \)
to be
\( 4 \cdot 6 \cdot 3 \)
.
\[\begin{aligned}
N = 7^3 \cdot 11^5 \cdot 41^2
\end{aligned}\]
Theorem. Consider the 4 digit number \( n = \overline{abcd} \) . \( n \) is divisible by 9 if the sum of its digits \( a + b + c + d \) is divisible by 9.
Proof. \[\begin{aligned} \overline{abcd} &= 1000a + 100b + 10c + d \end{aligned}\]\( \square \)
Note: \( \overline{abcd} \) means a 4 digit number.