Find if a Number is Divisible by 16

A brief tutorial which explains the divisibility rule for 16. Using this rule you could identify whether the given number is divisible by 16. The rule is illustrated with clear examples for easier understanding. Two rules are applied to check for the divisibility of 16. 'If the thousandth digit is even', Rule 1 is applied and 'If the thousandth digit is odd', then Rule 2 is applied.

Divisibility Rule for 16

Rule 1: If the thousandth digit is even
Steps to be Followed:

Consider the last 3 digits. Add the last two digits to four times the remaining number. If the result is divisible by 16, then the original number is also divisible by 16.

Rule 2: If the thousandth digit is odd
Steps to be Followed:

Consider the last 3 digits. Add 8 to it. If the result is divisible by 16, then the original number is also divisible by 16.

Example 1

Find if the number 254176 is divisible by 16

Solution :
Step 1:

Here thousandth digit is even (i.e) 4. As per Rule 1, add the last two digits to four times the remaining number (i.e) 1

(1 x 4) +76 = 80

Step 2:

Now it is clear that 80 is divisible by 16 (i.e) 80 = 5 x 16 Hence, the number 254176 is also divisible by 16

Example 2

Let us consider a number 23615 and find if the number is divisible by 16

Solution :
Step 1:

Here thousandth digit is odd (i.e) 3. As per Rule 2, add the last three digits to 8. 615 + 8 = 623

Step 2:

Now it is clear that 623 is not divisible by 16. Hence, the number 23615 is also not divisible by 16


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