Question

Using divisibility tests, determine the following number is divisible by 4, by 8.
572

Answer 1

Hint: In this particular type of question use the concept that according to divisibility rule of 4 if the last two digits (i.e. units place and tens place) of any number is divisible by 4 than the whole number is divisible by 4 so use this property to reach the solution of the question.

Complete step-by-step answer:
Given number:
572
Now we have to find out whether the above number is divisible by 4 or by 8 using the divisibility tests.
$\left( i \right)$ Divisibility rule of 4
According to the divisibility rule of 4 if the last two digits (i.e. units place and tens place) of any number is divisible by 4 then the whole number is divisible by 4.
This is because 100 is divisible by 4 so if we add any number say 24 in 100 we have 124, so we have to check only whether 24 is divisible by 4 or not if yes then the whole number is divisible by 4.
So in the given number 572 the last two digits is 72.
So divide 72 by 4 we have,
$ \Rightarrow \dfrac{{72}}{4} = 18$
So as we see that 72 is completely divisible by 4 so the whole number is divisible by 4.
$ \Rightarrow \dfrac{{572}}{4} = 143$
$\left( {ii} \right)$ Divisibility rule of 8
According to the divisibility rule of 8 if the last three digits (i.e. units place and tens place and thousand place) of any number is divisible by 8 then the whole number is divisible by 8.
As the given number is of 3 digits, so divide this by 8 we have,
$ \Rightarrow \dfrac{{572}}{8} = \dfrac{{143}}{2}$
So as we see that the number is not divisible by 8.
So this is the required answer.

Note: Whenever we face such types of questions the key concept we have to remember is that always recall the divisibility rule of 4 and 8 which is stated above and these rules are the basis to solve these types of questions and if we don’t remember the rule than divide some of the numbers directly and observe which rule it follows.