**Revision to this post. November 20, 2014**

**I woke up last night and to try to go to back to sleep I started dividing numbers in my head by 23. Found that I had missed a couple of multiples of 23 in the list below. My edits are in bold.**

To keep myself occupied when I walk through town, I like to factor three digit numbers. Since Oregon license plate identifiers have three numerical digits and three alphabetic characters, I have a “random” supply of numbers to factor. My current favorite three digit number is .

This is why divisibility tests have interested me. (See these last two posts: Divisibility by 13 and Divisibility by 17.) Generally when I wanted to factor a number I would just try dividing by various primes, but now, based on the understanding I gained exploring divisibility by 13 and 17, I have a systematic procedure. In outline, test a three digit number for divisibility by all primes through 19. **(Now 23)** If successful, divide out the prime and iterate. If no success, check to see if the number is one of six particular numbers.

First the six particular numbers. If a three digit number is not divisible by any prime number up through 19, then it could only be the product of primes and . These three digit numbers are . **Also 23 times 37 equals 851, 23 times 41 equals 943, and 23 times 43 equals 989. There are now too many numbers here. So I have added a divisibility test for 23 below.**

Use this divisibility test table for primes through . means divides with no remainder. Modulo means remainder after dividing by .

Divisibility Test Table for Three Digit Numbers

**For divisibility by 23 use 23|8a+10b+c.**

Here is an example.

Example: Factor 611

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## About jrh794

I am a sixty-five year old math instructor at Southern Oregon University. I taught at the College of the Siskiyous in Weed California for twenty-six years. Prior to that I worked as a computer programmer, carpenter and in various other jobs. I graduated from Rice University in 1967 and have a MS in Operations Research from Stanford. In the past I have hand-built a stone house and taken long solo bicycle tours. Now I ride my mountain bike and play golf for recreation.