Divisibility rules help us quickly determine if a number can be divided evenly by another without performing long division.
A number is divisible by 16 if any one of the following rules is satisfied.
Rule 1: (Last-Four-Digits Test)
Simply check whether the last four digits form a number divisible by 16.
For example: Check if 123456 is divisible by 16 or not.
- Given number is 123456, and last four digits are 3456
- 3456 ÷ 16 = 216 divisible
- so, 123456 is also divisible by 16
Rule 2: (Thousands–Digit Test)
For (EVEN):
If the thousands place digit is even,
- Take the last three digit of the number.
- The number formed by the last three digits must be divisible by 16.
For example: Check if 24832 is divisible by 16 or not.
- Thousands digit = 4 (even)
- Last 3 digits 832 ÷ 16 = 52
- Full number : 24832 ÷ 16 = 1552
The number 24832 divisible by 16
For (ODD):
If the thousands place digit is odd,
- Take the last three digit of the number.
- The last three digits must be equal to 8 times an odd number.
For example: Check if 123408 is divisible by 16 or not.
- Thousands digit = 3 (odd)
- Last 3 digits 408 ÷ 8 = 51
- Full number : 123408 ÷ 16 = 7713
The result is 408 divisible by 8 and return odd Quotient, so 123408 is also divisible by 16.
Rule 3: (Four-Times-the-Rest) Test
Separate the numbers into:
- R = all digits except the last two
- L = the last two digits
Compute 4R + L
If the result is divisible by 16, so is the original number.
For example: Check whether the number 1168 is divisible by 16 or not.
1,168
- R = 11,
- L = 68
4R = 4 ⨉ 11 = 44
Compare 4R + L = 44 + 68 = 112;
112 ÷ 16 = 7
Solved Questions on Divisibility Rule of 16
Example 1: Check if 2496 is divisible by 16 or not.
Solution:
Given number is 2496, the digit in thousand place is EVEN, so the Rule 1 should be applied.
- Last two digit = 96
- Hundreds place digit × 4 = 4 × 4 = 16
- Adding them we'll get, 96 + 16 = 112
The result 112 is divisible by 16, so 2496 is also divisible by 16.
Example 2: Check if 1536 is divisible by 16 or not.
Solution:
Given number is 1536, the digit in thousand place is ODD, so the Rule 2 should be applied.
- 8 + Last three digit = 8 + 536 = 544
The result 544 is divisible by 16, so 1536 is also divisible by 16.
Example 3: Check if 7830 is divisible by 16 or not.
Solution:
Given number is 7830, the digit in thousand place is ODD, so the Rule 2 should be applied.
- 8 + Last three digit = 8 + 830 = 838
The result 838 is not divisible by 16, so 7830 is also not divisible by 16.
Unsolved Questions on Divisibility Rule of 16
Question 1: Check if 432 is divisible by 16 using the divisibility rule.
Question 2: Check if 3,216 is divisible by 16 using the divisibility rule.
Question 3: Check whether the number 7,24,832 is divisible by 16 using the divisibility rule.
Question 4: Check whether the number 848 is divisible by 16 using the divisibility rule.