Hello, bware!
Are you aware of the various divisibility tests?
Decide wether the following are true of false using only divisibility test, give reason for the answer:
\(\displaystyle 24\;|\;325,608\)
\(\displaystyle N\,=\,325,608\)
The sum of the digits of \(\displaystyle N\) is divisible by 3 \(\displaystyle \,(3\,+\,2\,+\,5\,+\,6\,+\,0\,+\,8\:=\:24)\)
\(\displaystyle \;\;\) Hence, \(\displaystyle N\) is divisible by 3.
The last three-digit number of \(\displaystyle N\) is divisible by 8 \(\displaystyle \,(608\,\div\,8\:=\:76)\)
\(\displaystyle \;\;\)Hence, \(\displaystyle N\) is divisible by 8.
Therefore: \(\displaystyle N\) is divisible by: \(\displaystyle 3\cdot8\:=\:24\)
\(\displaystyle 45\,|\,13,075\)
The number ends in 5. \(\displaystyle \;\)Hence, \(\displaystyle N\) is divisible by 5.
But the sum of the digits, \(\displaystyle 1\,+\,3\,+\,0\,+\,7\,+\,5\:=\:16\), is not divisible by 9.
Therefore: \(\displaystyle N\) is
not divisible by 45.
\(\displaystyle 40\,|,1,732,800\)
Since \(\displaystyle N\) ends in 0, it is divisible by 5.
Since the last three-digit number is divislble by 8 \(\displaystyle \,(800 \,\div\,8\:=\:100)\), it is divisible by 8.
Therefore, \(\displaystyle N\) is divisible by: \(\displaystyle 5\cdot8\:=\:40\)
\(\displaystyle 36\,|\,677,916\)
The sum of the digits \(\displaystyle \,(6\,+\,7\,+\,7\,+\,9\,+\,1\,+\,6\:=\:36)\) is divisible by 9.
\(\displaystyle \;\;\)Hence, \(\displaystyle N\) is divisible by 9.
The last two-digit number is divisible by 4 \(\displaystyle \,(16\,\div\,4\:=\:4)\).
\(\displaystyle \;\;\)Hence, \(\displaystyle N\) is divisible by 4.
Therefore, \(\displaystyle N\) is divisible by: \(\displaystyle 9\cdot4\:=\;36\)
