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Published on September 29th, 2011 In category Division and Multiplication tricks | Education | Maths

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Prime number divisibility rules

The prime numbers are the numbers that have only 2 factors; 1 and number itself.

If we need to find, a large number is divisible by a prime number it is a bit of a problem.  We can get more factors of the number which needs to divide the bigger number. For example if we need to find if 31119 is divisible by 41 or not it is a bit of problem. 41 being a prime number can’t be subdivided.

Here are some easy rule for divisibility with the prime numbers:

Divisibility rule for 17

Separate the last digit, multiply by 5 and subtract from the truncated no.

Example: 1513 : 151 & 3, multiply 3 * 5 = 15, Subtract 151 – 15 = 136,  136 is divisible by 17, s0 1513 is divisible by 17

Divisibility rule for 19

Separate the last digit, multiply by 2 and add to the truncated no.

Example: 8588 : 858 &  8, multiply 8 * 2 = 16, add 858 + 16 =  874,  Repeat the process 87 & 4, multiply 4 * 2 = 8,  Add 87 + 8= 95, 95 is multiple of 19.

Divisibility rule for 23

Separate the last digit, multiply by 7 and add to the truncated no.

Example: 1035 : 103 & 5, multiply 5 * 7 = 35, Add 35 + 103 = 138,   23 * 6 = 138, s0 1035 is divisible by 23

Divisibility rule for 29

Separate the last digit, multiply by 3 and add to the truncated no.

Example: 1334 : 133 & 4, Multiply 4 * 3 = 12, Add 133 + 12 = 145,  29 * 5  =145 so 1334 is divisible by 29

Divisibility rule for 31

Separate the last digit, multiply by 3 and subtract from the truncated no.

Example: 1736:  173 &  6, Multiply 6 * 3 = 18, Subtract 173-18 = 155, clearly 155= 31 * 5 , so 1736 is divisible by 31

Divisibility rule for 37

Separate the last digit, multiply by 11 and subtract from the truncated no.

Example: 2849: 284 & 9, Multiply 11*9 = 99, Subtract 284- 99 = 185, clearly 185 = 37 * 5 , so 2849 is divisible by 37

Divisibility rule for 41

Separate the last digit, multiply by 4  and subtract from the truncated no.

Example: 2296; 229 & 6, Multiply 6 * 4 = 24, , subtract 229 – 24 = 205,  205 = 41 * 5, so 2296 is divisible by 41

Divisibility rule for 43

Separate the last digit, multiply by 13 and add to the truncated no.

Example: 3139 : 313 & 9, Multiply 13*9 = 117, Add 313 + 117 = 430, Quite clear, 3139 is divisible by 43

Divisibility rule for 47

Separate the last digit, multiply by 14 and subtract from the truncated no.

Example: 2632: 263 & 2, Multiply 2 * 14 = 28, Add 263 – 28 = 235,  Now 235 = 47 * 5 so 2632 is multiple of 47

IMPORTANT NOTE: If you get Zero then ignore and move on

This post has gone some lengthy next will publish the quiz based on this concept.

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