# Alternative explanation of divisibility rule for 7,11 and 13.

[ 7 ] Divide the number by 10. Subtract twice the remainder from the quotient. If the result is divisible by 7, the original number is also divisible by 7. For number with more than three digits, this method may continue till we get two digits. .....................................................e.g. 39573>> 3957 - 23=3951>>395-21=393>>39-2*3=33 not divisible by 7. So 39573 not divisible by 7. .... .. .....................................................................................................................................................................

[ 13 ] Divide the number by 10. Add four times the remainder to the quotient. If the result is divisible by 13, the original number is also divisible by 13. For number with more than four digits, this method may continue till we get two digits. e.g. 39573> 3957+43=3969>>396 +49=432>>43+4*2=51 not divisible by 13. So 39573 not divisible by 13. .. .. .

[ 11 ] Find the difference of sum of digits at the odd p[aces and sum at even places. If it is divisible by 11, the original number is also divisible by 11. e.g. 39 ]573>>3+5+3=11, 7+9=16. 16-11=5. 5 is not divisible by 11, so 39572 is also not divisible by 11.

[ 1001 ] 1001 is divisible by 7, 11,and 13........................e.g. 39573 -30030=9543 >>9543-8008=1537>>1537- 1001=536// :536>> 53-12=41 not divisible by 7...............536>>.. .6+5=11, 11 - 3 = 8 not divisible by 11.......536>>53+46=99 not divisible by 13....

Note by Niranjan Khanderia
5 years, 6 months ago

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Calvin Lin. Thanks for your appreciation.

- 5 years, 6 months ago