Question

Using the divisibility tests determine which of the following numbers are divisible by \[2\] .
A. \[2144\]
B. \[1258\]
C. \[4336\]
D. \[633\]
E. \[1352\]

Answer 1

Hint: In this question, we need to find which of the following numbers are divisible by \[2\] . First, we need to know the concept of the divisibility rule of \[2\] that is if a number ends in a \[0,2,4,6\] or \[8\], it is divisible by \[2\] . By using this property, we can check whether the number is divisible by \[2\] or not. Let us check the given numbers one by one whether the number is divisible by \[2\] or not.

Complete step-by-step answer:
Here we need to find the number which is not divisible by \[2\] from the following given numbers.
Divisibility rule for \[2\] :
The divisibility rule for \[10\] is nothing but if any number ends in a \[0,2,4,6\] or 8 then it is divisible by \[2\] .
First let us check the number \[2144\] whether it is divisible by \[2\] or not.
Now on observing the number \[2144\] , the unit digit of the number is \[4\] which is even .
Therefore the number \[2144\] is divisible by \[2\] .
Then we can check the number \[1258\] .
On observing the number \[1258\] , the unit digit of the number \[1258\] is \[8\] which is even .
Therefore the number \[1258\] is divisible by \[2\].
Next we can check the number \[4336\] .
On observing the number \[4336\], the unit digit of the number \[4336\] is \[6\] which is even .
Therefore the number \[4336\] is divisible by \[2\].
Then we can check the number \[633\] .
On observing the number \[633\], the unit digit of the number \[633\] is \[3\] which is odd .
Therefore the number \[633\] is not divisible by \[2\].
Finally we can check the number \[1352\] .
On observing the number \[1352\], the unit digit of the number \[1352\] is \[2\] which is odd .
Therefore the number \[1352\] is divisible by \[2\].
Thus the numbers \[2144\], \[1258\], \[4336\] and \[1352\] are divisible by \[2\] .
Final answer :
The numbers \[2144\], \[1258\], \[4336\] and \[1352\] are divisible by \[2\].
Option A, B, C, E are the correct answers.

Note: In order to solve these types of questions , we must always keep in mind the divisibility rule of the numbers to find out the results easily. The division rule is nothing but which helps us to check whether the given number is divisible by another number without using the actual method of division. We also need to know that if the number is completely divisible by another number then the quotient will be a whole number and the remainder will be zero.