Question

Find the largest \[4\] digit number divisible by \[16\].

Answer 1

Hint: We will first take the largest four-digit number and check whether it is divisible by sixteen or not, if it is divisible by sixteen then it will be the largest four-digit number divisible by sixteen.
If it is not divisible by sixteen then we will decrease the number one by one and check until we get the answer.

Complete step by step answer:
We aim to find the largest four-digit number that is divisible by sixteen.
Let us first take the largest four-digit number in the number system.
We know that \[9999\] is the largest four-digit number in the number system. Now let us check whether the number is divisible by sixteen or not.
\[9999 \div 16 = 624.9375\]
We got a decimal number which means that \[9999\] is not divisible by sixteen.
Now let us decrease the number by one so we get\[9999 - 1 = 9998\].
Now let us know whether \[9998\] is divisible by sixteen or not.
\[9998 \div 16 = 624.875\]
We got a decimal number which means that \[9998\] is not divisible by sixteen.
Now let us decrease the number by one again so we get\[9998 - 1 = 9997\]
Now let us know whether \[9997\] is divisible by sixteen or not.
\[9997 \div 16 = 624.8125\]
We got a decimal number which means that \[9997\] is not divisible by sixteen.
Now let us decrease the number by one again so we get \[9997 - 1 = 9996\]
Now let us know whether \[9996\] is divisible by sixteen or not.
\[9996 \div 16 = 624.75\]
We got a decimal number which means that \[9996\] is not divisible by sixteen.
Now let us decrease the number by one again so we get \[9996 - 1 = 9995\]
Now let us know whether \[9995\] is divisible by sixteen or not.
\[9995 \div 16 = 624.6875\]
We got a decimal number which means that \[9995\] is not divisible by sixteen.
Now let us decrease the number by one again so we get \[9995 - 1 = 9994\]
Now let us know whether \[9994\] is divisible by sixteen or not.
\[9994 \div 16 = 624.625\]
We got a decimal number which means that \[9994\] is not divisible by sixteen.
Now let us decrease the number by one again so we get \[9994 - 1 = 9993\]
Now let us know whether \[9993\] is divisible by sixteen or not.
Proceeding the above process, we get that \[9984\] as the answer for the given problem.
\[9984 \div 16 = 624\]
We got a whole number as an answer thus \[9984\] is the largest four-digit number divisible by sixteen.

Note: There is the shortest method to find the answer for this problem. First, we took the largest four-digit number and divided it by sixteen.
Then we have to round off the number we got.
Then multiplying this number by sixteen we get the solution for this problem.