Divisibility rule of 4, 8, and 16 with examples and practice questions

Divisibility Rule of 4, 8, and 16 – with Examples

Welcome to another divisibility rule tutorial. Today, we will discuss the divisibility rule of 4, divisibility rule of 8, and divisibility rule of 16. These rules are really interesting and you will never forget them if understood completely. Since 4,8, and 16 are even numbers and multiples of 2, a number should be even before you can check for its divisibility by these numbers.

If you’re looking for any other divisibility rules, please click here to get all the divisibility rules from 2 to 25.

Divisibility rule of 4

Divisibility rule of 4 written on a white background with division symbols on both sides

The divisibility rule of 4 states that, if the number formed by the last two digits of a number is a multiple of 4, then the entire number is divisible for 4.

Examples,

215596 is divisible by 4 as the number formed by the last two digits, i.e., 96, is a multiple of 4.

Similarly, 2029 is not divisible by 4 as 29 is not divisible by 4.

Divisibility rule of 8

The divisibility rule of 8 states, “if the number formed by the last 3 digits of a number is divisible by 8, then the entire number is also divisible by 8”.

Divisibility rule of 8 written in purple color on a white background

Examples,

For a number 51164352, the number formed by the last three digits, i.e., 352 is divisible by 8. Hence, the entire number 51164352 is also divisible by 8.

On the other hand, for the number 76910484, the number formed by the last three digits (i.e., 484) is not divisible by 8. Hence 76910484 is not divisible by 8.

Note:

The divisibility rule of 8 is helpful when you have large numbers (i.e., more than 5 digits). But to test for the three-digit numbers, here are some tips that you can follow:

  • Check if the three-digit number is divisible by 4, as it may only be divisible by 8 if the number is divisible by 4.
  • In that case, you can rule out any three-digit number which is not divisible by 4. For example, 126 is not divisible by 4 then it will never be disable by 8. Similarly, 256 is divisible by 4 then it may also be divisible by 8.

Divisibility rule of 16

The divisibility rule of 16 states, “If the number formed by the last 4 digits of a number is divisible by 16, then the entire number is divisible by 16”.

Divisibility rule of 16 written on a white background

For example, for a number 1279776, the number formed by the last 4 digits is 9776, which is divisible by 16 and gives 611 upon division. Hence, 1279776 is divisible by 16.

More divisibility rules of 16:

  • For smaller numbers, add the last two digits to the four times the rest. If the result is a multiple of 16, then the number is divisible by 16. i.e., for 256, 2×4 + 56 = 64, which is multiple of 16. Hence, 256 is also divisible by 16.
  • If in a number, a thousand digits is even, then the number formed by the last three digits must be divisible by 16. i.e., for 256272 with even at thousands place, 272 must be divisible by 16.
  • Also, if the thousand place digits is odd, then the number formed by the last three digits plus 8 must be divisible by 16. i.e., for 5136, 136+8 = 144 must be divisible by 16.

Tip: If a number is divisible by 4, only then it may be divisible by 16. If the number is not divisible by 4, it will not be divisible by 16.

Practice Questions for Divisibility Rule of 4, 8 and 16

Q. Without solving check the possibility of the following numbers being divisible by 4 or 8.
i. 123690
ii. 69991
iii. 2048
iv. 7772

Q. Check if the following numbers are divisible by 8.
i. 56998
ii. 36416
iii. 10348

Q. Which of the following number is divisible by 4 but not by 16.
i. 36416
ii. 23972
iii. 7992

Q. State True or False

  • If a number is divisible by 8 then it will also be divisible by 4.
  • A number can be divided by 16 only if it is divisible by both 4 and 8.
  • Only the even numbers can be divisible by 8.
  • If a number is a multiple of 4 and 2, then it can be divided by 8.

Check more divisibility rules:

Divisibility rule of 12Divisibility rule of 13
Divisibility rule of 17Divisibility rule of 18
Divisibility rule of 15Divisibility rule of 25

Thanks for your time! I hope you have understood the divisibility rule of 4, 8, and 16. Make sure to practice enough to keep these rules inside your mind. You can solve previous question papers if you’re preparing for any exam or can get a quantitative aptitude book to practice more. You can explore many sample papers and books at really great discounts here.

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