Divisibility Rule for 19 Proof and Examples - How do you Test Divisibility by 19?

Divisivility Rules are simple tricks by which you can decide whether a number is divisible by another number or not without even performing the division actually. In this article of ours, we will explain about Divisibility Rule for 19, How to Tell if a Number is Divisible by 19 or not, and Solved Examples on Testing Divisibility. Learn the simple tricks to decide whether a particular number is divisible by 19 or not no matter how large the number is.

What is the Divisibility Rule of 19?

If the sum of twice the last digit and the remaining digits of the number is divisible by 19 then the number is divisible by 19. In the case of a larger number if the sum of 4 times the last digit and remaining digits is divisible by 19 then the given number is divisible by 19. These two are the divisibility rules for 19.

How to Find if a Number is Divisible by 19 or Not?

See the step-by-step procedure to check if a number is divisible by 19 or not. They are along the lines

Rule 1:

  • Multiply the unit digit by 2.
  • Add the result to the remaining digits of the number.
  • If the resultant value is divisible by 19 then the given number is divisible by 19.

Rule 2:

  • Multiply the unit digit by 4.
  • Find the sum of the unit digit by 4 and the remaining digits of the number.
  • Apply this rule again and again until the sum is easily divisible by 19 and if the result is divisible the entire number is divisible by 19 or not.

Divisibility Rule for 19 Proof

We will prove the Divisibility of 19 by considering an example.

Let us say we have the number 475

The number at units place = 5

Now multiply it with 2 and add to the remaining number = 47+5 x 2

= 47 +10

= 57

Dividing it with 19 we get 57/19 = 3

As the result is divisible we can say that the entire number is divisible by 19.

Hence Proved.

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What numbers are divisible by 19

List of Numbers divisible by 19: The Numbers 19, 38, 57, 76, 95, 114, 133, 152, 171, 190, 209, 228, 247, 266, 285, 304, 323, 342, 361, 380, 399, 418, 437, 456, 475, 494, 513, 532, 551, 570, 589, 608, 627, 646, 665, 684, 703, 722, 741, 760, 779, 798, 817, 836, 855, 874, 893, 912, 931, 950, 969, 988, 1007, 1026, 1045, 1064, 1083, 1102, 1121, 1140, 1159, 1178, 1197, 1216, 1235, 1254, 1273, 1292, 1311, 1330, 1349, 1368, 1387, 1406, 1425, 1444, 1463, 1482, 1501, 1520, 1539, 1558, 1577, 1596, 1615, 1634, 1653, 1672, 1691, 1710, 1729, 1748, 1767, 1786, 1805, 1824, 1843, 1862, 1881, 1900, etc. are divisible by 19.

FAQs on Divisibility Test for 19

What is the trick to check the divisibility by 19?

The trick to check the divisibility by 19 is to find the sum of twice the last digit and the remaining numbers and then divide by 19. If the result is divisible by 19 the number is divisible by 19.

Is 171 divisible by 19?

Yes, 171 is divisible by 19.

Which is the largest three-digit number that is divisible by 19?

The largest three-digit number that is divisible by 19 is 988.

Wrapping Up

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