Year 8 Interactive Maths - Second Edition

Problem Solving Unit

Problem 4.1  Perfect Number

A perfect number is a number that is equal to the sum of all its factors except for the number itself.

So, the factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248 and 496.

Thus, 496 is a perfect number as the sum of all its factors (excluding the factor 496) is equal to 496.

1.  Find the smallest perfect number.

2.  Find the next perfect number.

3.  Show that the following numbers are perfect numbers:
a.  8128
b.  3 335 036