Divisibility by \(4\):
If a last two digits of any number are divisible by \(4\), then that number is divisible by \(4\).
Example:
Consider the number \(248\).
In this, the last two digits are \(48\).
\(\frac{48}{4} = 12\)
Thus, \(248\) is divisible by \(4\).
Divisibility by \(5\):
If a digit in the ones place of a number is \(5\) or \(0\), then it is divisible by \(5\).
Example:
Consider the number \(3270\).
In this, the last digit is \(0\).
Thus, \(3270\) is divisible by \(5\).
Divisibility by \(7\):
Double the last digit of the number and then subtract it from the remaining number if the number formed is divisible by \(7\), then the number is divisible by \(7\).
For example, consider \(294\).
Doubling the last digit \(4\), we get \(4 \times 2 = 8\)
Subtracting \(8\) with the remaining digits, we have \(29 - 8 = 21\)
Now, \(\frac{21}{7} = 3\)
Thus, the number \(294\) is divisible by \(7\).
Divisibility by \(8\):
A number is divisible by \(8\) if the number formed by its last three digits is divisible by \(8\).
Example:
Consider the number \(35416\).
Consider the last three digits \(416\). Here, \(\frac{416}{8} = 52\).
Since \(416\) is divisible by \(8\), the number \(35416\) is divisible by \(8\).
Divisibility by \(10\):
A number is divisible by \(10\), if it ends with \(0\).
Example:
Consider the number \(3320\).
In this, the last digit is \(0\).
Thus, \(3320\) is divisible by \(10\).