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....

#NumberTheory #RulesOfDivisibility

Note by Niranjan Khanderia
6 years, 5 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list
  • bulleted
  • list

1. numbered
2. list
  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai−1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 ∑i=13 \sum_{i=1}^3
\sin \theta sin⁡θ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Calvin Lin. Thanks for your appreciation.

Niranjan Khanderia - 6 years, 5 months ago
×

Problem Loading...

Note Loading...

Set Loading...