Tanya Khovanova’s Math Blog » Blog Archive » Divisibility by 7 is a Walk on a Graph, by David Wilson. My guest blogger is David Wilson, a fellow fan of sequences. It is a nice exercise to understand how this graph works. When you do, you will discover that you can use this graph to calculate the remainders of numbers modulo 7. Back to David Wilson: I have attached a picture of a graph. Write down a number n. For example, if n = 325, follow 3 black arrows, then 1 white arrow, then 2 black arrows, then 1 white arrow, and finally 5 black arrows.
If you end up back at the white node, n is divisible by 7. Nothing earth-shattering, but I was pleased that the graph was planar. Doodling in Math Class: Infinity Elephants. Happy Saint Math Tricks Day 2011. Time Well Spent. Sugar, Sugar - Xmas Special. Nerd Paradise : Divisibility Rules for Arbitrary Divisors. It's rather obvious when a number is divisible by 2 or 5, and some of you probably know how to tell if a number is divisible by 3, but it is possible to figure out the division 'rule' for any number. Here are the rules for 2 through 11... The last digit is divisible by 2. The sum of all the digits in the number is divisible by 3. The last 2 digits are divisible by 4. The last digit is 5 or 0. The number is both divisible by 2 and divisible by 3. Cut the number into 2 parts: the last digit and everything else before that. The last 3 digits are divisible by 8 The sum of all the digits in the number is divisible by 9.
The last digit is a 0. Break the number into two parts (like you did for the division by 7 rule). Also there is a quick way for determining divisibility by 11 for 3-digit numbers: If the inner digit is larger than the two outer digits, then it is divisible by 11 if the inner digit is the sum of the two outer digits. Rules for all divisors ending in 1... User Comments: 9 Dividing By 12. What's Special About This Number? HeartCurves_801.gif (GIF Billede, 455x306 pixels)