Divisibility Rule for 17 with Examples - How to Check Divisibility by 17?

Divisibility Rule of 17 is taught here in detail. If you are facing any trouble solving the problems on the division of large numbers by 17 then this page will give you all that you need to know about the tricks. Read more to study the Divisibility Rule for 17, How to Test if a Number is Divisible by 17 or not, and Solved Examples on Divisibility by 17. You need not divide the number manually and by following these simple tips you can decide whether the number is divisible by 17 or not.

What is the Divisibility Rule of 17?

As per the divisivility rule of 17, a number is divisible by 17 if the last digit of the number when multiplied by 5 and subtracted from the rest is divisible by 17. For example, let us take 745. 74 - 5*5 = 74-25 = 49 49 is not divisible by 17. So 745 is not divisible by 17.

How to Determine if a Number is Divisible by 17?

Go through the simple process mentioned below to see if a Number is divisible by 17 or not. They are along the lines

  • Firstly, multiply the last digit of the given number by 5.
  • Then, subtract the result from the remaining digits.
  • If the result is divisible by 17 then the given number is also divisible by 17.

To better understand this concept of the Divisibility Test of 17 we have given a few worked-out examples.

Worked Out Examples on Divisibility Test of 17

Example 1:

Is 985 divisible by 17?

Solution:

Given number is 985

Multiply last digit by 5 i.e. 5 x 5 = 25

Subtract the result obtained above from the remaining number i.e. 98 - 25 = 73

Since 73 is not divisible by 17 the entire number 985 is not divisible by 17.

Example 2:

Is 1234 divisible by 17?

Solution:

Given number is 1234

Multiplying the last digit by 5 we have 4 x 5 = 20

Subtract the result from the remaining number i.e. 123 - 20 = 103

103/ 17

17 will not go completely in 103

Thus, the number 1234 is not divisible by 17.

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What numbers are divisible by 17

List of Numbers divisible by 17: The Numbers 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 272, 289, 306, 323, 340, 357, 374, 391, 408, 425, 442, 459, 476, 493, 510, 527, 544, 561, 578, 595, 612, 629, 646, 663, 680, 697, 714, 731, 748, 765, 782, 799, 816, 833, 850, 867, 884, 901, 918, 935, 952, 969, 986, 1003, 1020, 1037, 1054, 1071, 1088, 1105, 1122, 1139, 1156, 1173, 1190, 1207, 1224, 1241, 1258, 1275, 1292, 1309, 1326, 1343, 1360, 1377, 1394, 1411, 1428, 1445, 1462, 1479, 1496, 1513, 1530, 1547, 1564, 1581, 1598, 1615, 1632, 1649, 1666, 1683, 1700, etc. are divisible by 17.

FAQs on Divisibility by 17

  1. What is the Divisibility Test of 17?

Divisibility Test of 17 states that a number is divisible by 17 when the result you obtain after subtracting the last number multiplied by 5 from the remaining number is divisible by 17.

  1. How to Check Divisibility Test for 17?

Simply multiply the last digit of the number by 5, subtract the result from the remaining number and see if the result you obtain is divisible by 17 or not. If it is divisible the number is divisible by 17.

  1. What is the largest 3-digit number that is divisible by 17?

The largest 3-digit number that is divisible by 17 is 986.

Summary

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