Check the Divisibility by prime numbers

Divisibility rule 7, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

This note has been used to help create the Divisibility Rules of prime number because checking the divisibility by prime number has some different rules as compared to checking divisibility by composite number. Here you will know how to check divisibility by a prime number. Some rules you will have to learn for checking it. We have explained it step by step.

Check the divisibility by 7:

For checking divisibility by 7, Subtract 2 times the last digit from the remaining number. Repeat the step as necessary. If the result is divisible by 7, the original number is also divisible by 7

Example: Check for 959:

Multiply unit digit 9 by 2 ant subtract it with the remaining number. 9*2=18. Now the remaining number is 95. Subtract 18 with 95.

95-(2*9)=77. Since 77 is divisible by 7, the original no. 959 is also divisible.

Check the divisibility by 13:

For checking divisibility by 13, Add 4 times of the last digit to the remaining number. Repeat this step as necessary. If the result is divisible by 13, the original number is also divisible by 13.

Example: 4134:: 413 + (16) = 429::

Now repeat this step because to check 429 directly will be a difficulty so we repeat this process. Multiply 9*4=36 add it with the remaining number and again check.

Example: 42+(36) = 78. Since 78 is divisible by 13, the original no. Hence 4134 is also divisible

Check the divisibility by 17:

For checking divisibility by 17, Subtract 5 times the last digit from the remaining number. Repeat the step as necessary. If the result is divisible by 17, the original number is also divisible by 17

Example: 7905:: 790-(5*5)=765. Since 187 is divisible by 17, the original number 2278 is also divisible.

Check the divisibility by 19:

Add 2 times the last digit to the remaining truncated number. Repeat the step as necessary. If the result is divisible by 19, the original number is also divisible by 19

Example: 11343:: 1134+(23)= 1140. (Ignore the 0):: 11+(24) = 19. Since 19 is divisible by 19, original no. 11343 is also divisible

Chec the divisibility by 23:

Add 7 times the last digit to the remaining truncated number. Repeat the step as necessary. If the result is divisible by 23, the original number is also divisible by 23

Example: 53935:: 5393 + (75) = 5428 :: 542 + (78)= 598:: 59+ (7*8) = 115, which is 5 times 23. Hence 53935 is divisible by 23

Chec the divisibility by 29:

Add 3 times the last digit to the remaining truncated number. Repeat the step as necessary. If the result is divisible by 29, the original number is also divisible by 29

Example: 12528:: 1252 + (38)= 1276 :: 127 + (36)= 145:: 14 + (3*5)=29, which is divisible by 29. So 12528 is divisible by 29

Chec the divisibility by 31:

Subtract 3 times the last digit from the remaining truncated number. Repeat the step as necessary. If the result is divisible by 31, the original number is also divisible by 31

Example:r 49507:: 4950 – (37)=4929 :: 492 – (39) :: 465:: 46 – (3*5)=31. Hence 49507 is divisible by 31

Check the divisibility by 37:

Subtract 11 times the last digit from remaining truncated number. Repeat the step as necessary. If the result is divisible by 37, the original number is also divisible by 37

Example: 11026:: 1102 – (116) = 1036. Since 103 – (116) = 37 is divisible by 37. Hence 11026 is divisible by 37

Check the divisibility by 41:

Subtract 4 times the last digit from the remaining truncated number. Repeat the step as necessary. If the result is divisible by 41, the original number is also divisible by 41

Example: 14145:: 1414 – (45) = 1394. Since 139 – (44) = 123 is divisible by 41. Hence 14145 is divisible by 41

Check the divisibility by 43:

Add 13 times the last digit to the remaining truncated number. Repeat the step as necessary. If the result is divisible by 43, the original number is also divisible by 43.*This process becomes difficult for most of the people because of multiplication with 13.

Example: 11739:: 1173 + (13*9)= 1290:: 129 is divisible by 43. 0 is ignored. So 11739 is divisible by 43

Chec the divisibility by 47:

Subtract 14 times the last digit from the remaining truncated number. Repeat the step as necessary. If the result is divisible by 47, the original number is also divisible by 47. This too is difficult to operate for people who are not comfortable with the table of 14.

Example: 45026:: 4502 – (146) = 4418. Since 441 – (148) =329, which is 7 times 47. Hence 45026 is divisible by 47

I hope, this article will help you a lot to understand the Check the Divisibility by prime numbers. If you still have any doubts and problems with any topic of mathematics you can ask your problem in the Ask Question section. You will get a reply shortly.

Related Topic:

Divisibility Rules | How to Check the divisibility of number

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