Question

Prove that an integer is divisible by 4 if and only if the number formed by its tens and units digits is divisible by 4.

Answer 1

Answer:

Kindly refer to below section.

Step-by-step explanation:

Any number $pqr$ can be represented as:

$pqr=100p+10q+r$

For example a number 78332 can be represented as:

$78332 = 100\times 783+10\times 3+2$

Let any number be $pqr$ and the number formed by its tens and units digits is divisible by 4.

i.e. $10q+r$ is divisible by 4.

$\therefore 10q+r=4k$

Now, the number $pqr$ can be written as:

$pqr=100p+4k\\\Rightarrow pqr=4(25p+k)$

Therefore, $pqr$ is also divisible by 4.

Hence, proved that an integer is divisible by 4 if and only if the number formed by its tens and units digits is divisible by 4.