How can you tell if a number is divisible by four?
If the last two digits of the number are divisible by four then the original number is also divisible by 4.
For example, if the number is 47,128 then the last two digits of that number is 28. As 28 is not divisible by 4 the original number 47,128 is not divisible by four .
Why Does This Method Work?
The reason why this method works is that the multiples of four reset at every hundred. Therefore, if you start at four and progress by 4’s you’ll hit 100.
This means that every number larger than 100 that is a multiple of 4: 112, 212, 312, 412, 512, 6,012, 77,712 are all multiples of 4! To know then if a number is a multiple of four you only need focus on the last two.
Can You Find It Faster?
Is there a way of finding if a number is a multiple of four even faster than trying to divide the last two digits by four and seeing if it has no remainder?
Looking at the multiples of 4 you will also notice that the last digit resets at every 20.
This means the multiples of 4 between 0 and 9 will have the same final digit at each 20 cycle, and the multiples of 4 between 10 to 19 will have the same final digit at each cycle of 20.
Therefore, if the last digit is 0, 4 and 8 and the second-last digit (the tens digit) is even then the number is a multiple of 4.
However, if the last digit is 2 or 6 and the second-last digit (again, the tens digit) is odd then the number is a multiple of 4.
Here are some examples explaining this step by step.
Is the number 8,264 divisible by 4?
The tens digit is even , therefore if the last digit is either 0, 4 or 8 then the number is a multiple of 4. In this case the final digit is 4, therefore 8,264 is a multiple of 4.
What about the number 63,216 – is this number divisible by 4?
As the tens digit is odd if the last digit is 2 or 6 then the number is a multiple of 4. As the last digit is 6 the number 63,216 is divisible by 4.
Exercises And Answers
Have a go at the following list of numbers and see how you go in finding out if they are divisible by 4.
(Answers will be underneath, see if you can time yourself at how quickly you get through them all)
- 180
- 2,052
- 86,668
- 108,534
- 7,245,676
- 12,643,708
- 435,765,542
How did you go with those numbers? We’re you able to easily see if they were divisible by 4?
Here are the answers:
- Yes, tens digit is even and last digit is 8.
- Yes, tens digit is odd and the last digit is 6.
- Yes, tens digit is even and the last digit is 8.
- No, tens digit is odd and the last digit is not 2 or 6.
- Yes, tens digit is odd and the last digit is 6.
- Yes, tens digit is even and the last digit is 8.
- No, tens digit is even and the last digit is not 0, 4 or 8.
Summary
A number is divisible by 4 if the last two digits of the number are itself divisible by 4.
A faster way of knowing is if the tens digit of the original number is even and the last number is either 0, 4 or 8 then the original number is divisible by 4. If the tens digit is odd and the last number is either 2 or 6 then the original number is divisible by four.
Next, you might want to check how you can quickly find if a number is divisible by 3 .