You may be aware of divisibility tests for numbers like 3 ,4,5,8,9,16 etc.
I now present you with a combined divisibility test for 7,11 and 13.
I am taking the number128704719 for the test.
You divide it into groups of 3 digits starting from the right.Call the groups A,B,and C.Thus A=719,B=704 and C=128.Add up the figures in alternative groups and find the difference between those sums.Thus A+C=847.For B there is no further group to add and so the sum is the same number as B viz 704.The difference between the sums is thus 847-704=143.Test this result for divisibility by 7 ,11, and 13.If it is divisible the original number will also be divisible.As 143 is divisible by 11 and 13 and not by 7 the original number 128704719 will be divisible by 11 and 13 and not by 7.
Actually 128704719= 11 times 11700429 and 13 times 9900363 while division by 7 gives a quotient 18386388 and a remainder 3.
When you take a number with say10 or 11 digits for test you will have a group D which can be added to B
This method is based on the fact that the product of 7,11 and 13 is 1001.
If the factors of numbers like 1001 are known,you can find similar procedures for testing .Example 1003 has the factor 17.-can be used for testing divisibility by 17....1007 has the factor 19-can be used for 19.. .
I now present you with a combined divisibility test for 7,11 and 13.
I am taking the number128704719 for the test.
You divide it into groups of 3 digits starting from the right.Call the groups A,B,and C.Thus A=719,B=704 and C=128.Add up the figures in alternative groups and find the difference between those sums.Thus A+C=847.For B there is no further group to add and so the sum is the same number as B viz 704.The difference between the sums is thus 847-704=143.Test this result for divisibility by 7 ,11, and 13.If it is divisible the original number will also be divisible.As 143 is divisible by 11 and 13 and not by 7 the original number 128704719 will be divisible by 11 and 13 and not by 7.
Actually 128704719= 11 times 11700429 and 13 times 9900363 while division by 7 gives a quotient 18386388 and a remainder 3.
When you take a number with say10 or 11 digits for test you will have a group D which can be added to B
This method is based on the fact that the product of 7,11 and 13 is 1001.
If the factors of numbers like 1001 are known,you can find similar procedures for testing .Example 1003 has the factor 17.-can be used for testing divisibility by 17....1007 has the factor 19-can be used for 19.. .
neat...thats an elegant test for divisibility!!
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