Divisibility Rule of 17, 18, and 19 – with Examples

Divisibility rule of 17

The divisibility rule of 17 states, “If the difference between 5 times the last digit and the rest is either 0 or multiple of 17, then the number is divisible by 17”.

For example, for 289, (9×5) – 28 = 17. Hence, 289 is divisible by 17.

More divisibility rules of 17

Apart from the above rule, there are some more rules of divisibility for 17. You can use any of the rule depending upon your understanding and the given number.

Let’s check these too:

Alternate Rule 1: If the difference between the number formed by the last two digits and two times the rest is either 0 or a multiple of 17, then the number is divisible by 17. i.e., for 289, 89 – (2×2) = 85, which is multiple of 17.

Alternate Rule 2: If the sum of 9 times the last digit and 5 times the rest is divisible by 17 then the number is divisible by 17. i.e., for 289, 28 x 5 + 9×9 = 221, which is divisible by 17.

With this rule, you can reduce a large number to a smaller number. But, for smaller numbers, it may take extra time and may not be recommended.

You might want to check: Maths formulas for Class 10

Divisibility rule of 18

The divisibility rule of 18 states, “If a number is divisible by both 2 and 9, then the number is also divisible by 18.”

You can test for the divisibility by 2 and 9 by following the divisibility rule of 2 and the divisibility rule of 9.

For example, let’s test the divisibility of 10242 by 18.

As the last digit is 2, the number is divisible by 2. Also, the sum of all digits, 1+0+2+4+2 = 9. Hence, 10242 is divisible by 18 and gives 569 upon division.

Since the divisibility rule of 18 depends upon the divisibility rule of 2 and 9, there are some important points to remember while testing the divisibility by 18. These points will save time while testing the divisibility of a number:

• Start with the smaller number, i.e., check if the number can be divided by 2 first. If not, there is no need to proceed with 9.
• If possible try to memorize the table of 18 for a quick solution of smaller 3-digit numbers.
• You can memorize that every number that is divisible by 18 must have 8,6,4,2 or 0 at one’s place. Later, all you need to do is check the divisibility for 9.

Divisibility rule of 19

The divisibility rule of 19 states, “If the sum of twice the unit digit and the remaining number is divisible by 19, then the entire number is said to be divisible by 19”.

If a number is larger, follow the below steps:

• Add 4 times the last two digits (one’s and ten’s) to the remaining number
• If the result is a multiple of 19, then the number is divisible by 19.
• If the sum is still a large number, you can repeat any of the rules to reduce it or test the divisibility.

i.e., for 361, 36 + 1 x 2 = 38 which is divisible by 19. Hence, 361 is divisible by 19.

Tip: For large numbers, repeat the process as required.

For example, let’s check the divisibility of 2337.

233 + 2×7 = 247, 24 + 2×7 = 38, which is multiple of 19. Hence, 2337 is divisible by 19.

Also, 23 + 37×4 = 171, 17 + 2×1 = 19.

Wasn’t that so simple?

Practice Questions for Divisibility rule of 17, 18, and 19

Q. Test the divisibility of the following numbers by 17, 18, and 19.

• 5814
• 12240
• 3876
• 7695
• 2345778
• 610470
• 54418

Q. What is the least number that should be added to 5500 to make it divisibly by 17 and 18 but not by 19.
Q. What is the least number that should be subtracted from 17460 to make it divisibly by 17, 18, and 19.

More divisibility rules

Divisibility rule of 9	Divisibility rules of 7
Divisibility rules of 25	Divisibility rule of 15
Divisibility rule of 16

That was all about the divisibility rule of 17, 18, and 19. You can learn these rules and practice regularly to memorize for a quick solution while attempting the exam. For the latest updates, you can connect with us on Facebook or Instagram.