Callaghan Numbers

Sometimes I have trouble trying to get to sleep because my brain is always thinking about something. The other night when I couldn’t get to sleep I discovered a new set of numbers. I have called them Callaghan Numbers. When I woke up the next morning, I couldn’t wait to tell my Dad about my discovery (my Dad is a maths nerd like me). I was jumping out of my wheelchair that morning while I explained this awesome discovery. My Dad and my Mum were proud of my new finding.

So, let me explain it to you. A callaghan number is a number whose factors all multiply to make the square of that number.  (A factor of a given number is any whole number that divides evenly into the original number). The only callaghan numbers known are 0, 1, 6, 8, 10, 14, 15, 22, 26, 27, 33, 34, 35, 38, 39, 46, 49, 55, 57, 58, 62, 65, 69, 77. For example: take the number 8. Its factors are 1, 2, 4, 8.

If you multiply 1 x 2 = 2,

2 x 4 = 8,

8 x 8 = 64 and 64 is the square of 8.

Tadaa! Now you have a callaghan number!

Try it out for some of the other callaghan numbers and let me know how you go. I will give a shout out to anyone who finds more Callaghan Numbers and shares them along with the proof.

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1 Comment

  1. Wowzee! Love the Callaghan numbers, you are very clever. I will let you know if I work out any new Callaghan numbers


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