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Abundant Numbers III


A whole number is called abundant if the sum of its factors, excluding itself, is more than the number. For example, 18 is an abundant number, since the sum of its factors excluding itself (1 + 2 + 3 + 6 + 9) equals 21, which is more than 18. What are the five smallest abundant numbers? What do these numbers have in common?

(Source: Adapted from Mathematics Teaching in the Middle School, Sep-Oct 1996)


 Extensions

A whole number is called perfect if the sum of its factors, excluding itself, is equal to the number. For example, 6 is a perfect number since the sum of its factors excluding itself (1 + 2 + 3) equals 6. What are the five smallest perfect numbers?



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