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St Francis de SalesCatholic Junior School

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12/10/2018 - The Perfect Number!

Abundances, Deficiencies and the Perfect Number!

Picture 1

'Today, in Maths, we started to recap primes and factors. After realising that we were secure in this area, Mr Kennedy challenged us to advance to something we had never even heard of: deficient numbers, abundant numbers and perfect numbers!


To work out a deficient number, we had to find the proper divisors of a number (this means all of its divisors, except the number itself) and add them together. If this totalled less than the number, then it is a deficient number. A number is abundant if its proper divisors are larger than the number itself. We noticed that 6 and 28 had proper divisors that totalled 6 and 28. These are called perfect numbers and have mystified mathematicians since the days of Ancient Greece! 


For example: the proper divisors of 6 are: 1, 2 and 3 - we do not include the original number. If you add 1, 2 and 3 together, then you equal 6, meaning it is a perfect number!


Did you know that no prime numbers can be abundant?

Did you know that abundant numbers are more likely to be even? The first odd abundant number is 945!

If you find an abundant number, then all of its multiples are also abundant. For example, because 12 is an abundant number, so is are 24, 36, 48 etc. 


I really enjoyed this lesson!'


Jessica, Isabelle, Ruby, Christy and Leo.