# Fast division by 23 **URL:** \ **Category:** Mental Calculation, Mathematics, and Puzzles\ **Created:** [October 15, 2017, 7:57am UTC](https://forum.artofmemory.com/t/fast-division-by-23/32967 "2017-10-15T07:57:54Z")\ **Posts on this page:** 1\ **Showing post:** 4
**Author:** ![Kinma](https://forum.artofmemory.com/letter_avatar_proxy/v4/letter/k/a88e4f/32.png) [@Kinma](https://forum.artofmemory.com/u/Kinma)\ **Post date:** [October 24, 2017, 7:27am UTC](https://forum.artofmemory.com/t/fast-division-by-23/32967/4 "2017-10-24T07:27:19Z")
> [@Nodas](#): > > But besides such brute-force division, one could also instead memorize the cycle of 23. This has just 11 repeating digits, in particular: 04347826086 and then continue with their exact complements (to 9) respectively: 95652173913. So true. > [@Nodas](#): > > And since this is a primarily memory forum, I think it’s useful to incorporate some extra memory tricks into calculation. This is true and can do with a bit of repeating. We have talked about this in the past. Like here: > **[Analyzing Rüdiger Gamms performance (division by 109)](https://forum.artofmemory.com/t/analyzing-rudiger-gamms-performance-division-by-109/28101)** > > While watching YouTube videos’of Rüdiger Gamms performance in order to find out how he does the higher powers I realized something. In at least three video’s I saw him do a division by 109. There is a reason for this. One example is this video: ... > **[Analyzing Rüdiger Gamms performance (division by 167)](https://forum.artofmemory.com/t/analyzing-rudiger-gamms-performance-division-by-167/28102)** > > We had some fun analyzing Rüdiger Gamms performance in his division by 109. Now let’s see how one can easily do the division by 167 in this video (starts at 0:00): If you did not watch the video, he calculates: 62/167. I have an... > [@GreyMatters](#): > > Alternative method for dividing by 23: Multiply the dividend by 3, and then divide it by 69, using the technique for dividing by numbers ending in 9. > > So, 100/23 becomes 300/69, and you still get the same answer. Excellent find! That works just as well of course. One of the things I like in mental calculation is that there are usually even simpler ways of calculating. Creativity is so important! --- _[View the full topic](https://forum.artofmemory.com/t/fast-division-by-23/32967)._