Tag Archives: factorization

Fast and slow machines

Posted on January 27, 2018 by Brent

In my previous post, I presented three hypothetical machines which take a positive integer as input and give us something else as output: a factorization machine gives us the complete prime factorization of ; a factor machine gives us one … Continue reading →

Posted in computation, number theory, primes | Tagged , , , , , , , , , , | 1 Comment

A tale of three machines

Posted on January 3, 2018 by Brent

The Fundamental Theorem of Arithmetic tells us that any positive integer can be factored into a product of prime factors.1 Given a positive integer , this leads naturally to several questions: What is the prime factorization of ? This is … Continue reading →

Posted in computation, number theory, primes | Tagged , , , , | 11 Comments

The Riemann zeta function and prime numbers

Posted on March 6, 2017 by Brent

In a previous post I defined the famous Riemann zeta function, Today I want to give you a glimpse of what it has to do with prime numbers—which is a big part of why it is so famous. Consider the … Continue reading →

Posted in number theory | Tagged , , , , | 15 Comments

Games with factorization diagram cards

Posted on February 17, 2017 by Brent

Since I published a deck of factorization diagram cards last September, a few teachers have picked up copies of the cards and started using them with their students. I’ve started collecting ideas for games you can play using the cards, … Continue reading →

Posted in arithmetic, counting, games, pattern, pictures, primes, teaching | Tagged , , , , , | 4 Comments

Factorization diagram cards are here!

Posted on September 11, 2016 by Brent

It’s been a long process, but factorization diagram cards are finally available for purchase! If you just want to purchase a set right this minute, then click the above link! If you want to learn more, keep reading. History As … Continue reading →

Posted in arithmetic, counting, pattern, pictures, primes, teaching | Tagged , , | 2 Comments

Factorization diagram card redesign: feedback welcome!

Posted on August 24, 2016 by Brent

After getting a printed set of factorization diagram cards, I decided there were a few design tweaks I wanted to make. I’ve gone through a few iterations and I think they are definitely better now. Here are some representative samples … Continue reading →

Posted in arithmetic, counting, pattern, pictures, primes, teaching | Tagged , , | 6 Comments

Factorization diagram cards!

Posted on May 31, 2016 by Brent

I’ve designed a set of factorization diagram cards and had them actually printed. This is one of the first times in my life when I have caused Actual Physical Objects to be created (other than using a printer I guess) … Continue reading →

Posted in arithmetic, counting, pattern, pictures, primes, teaching, video | Tagged , , | 5 Comments

Factorization diagram posters!

Posted on December 13, 2013 by Brent

I’ve finally gotten around to making a nice factorization diagram poster: You can buy high-quality prints from Imagekind. (If you order soon you should have them before Christmas! =) I’m really quite happy with imagekind, the print quality is fantastic … Continue reading →

Posted in arithmetic, counting, geometry, number theory, pattern, pictures, primes | Tagged , , | 7 Comments

Factorization diagram cards: help?

Posted on February 5, 2013 by Brent

The other day I got a lovely email from Malke Rosenfeld thanking me for creating factorization diagrams and linking me to her blog post about “factor dominoes”: she printed out some factorization diagrams, glued them to cardstock, and used the … Continue reading →

Posted in arithmetic, pictures, primes | Tagged , , , | 2 Comments

More factorization diagrams

Posted on November 5, 2012 by Brent

My post on factorization diagrams from a month ago turned out to be (unexpectedly) quite popular! I got ten times as many hits as usual the day it was published, and since then quite a few other people have created … Continue reading →

Posted in arithmetic, links, pictures, primes, programming, recursion | Tagged , , | 15 Comments