Program 24

C++

K. Dzwonkiewicz

The factors of a number that are less than that number are called the proper factors (all factors besides the number).

In ancient Greece (500 BC), Pythagoras ran a school (PCMST) for philosophy, science, mathematics, and cooking. His students were fanatical about learning. They became a cult that existed for 300 years. They thought everything in life could be defined mathematically. Harmony of a person’s life was calculated with a formula…all thongs were measurable. In theory this may sound plausible, but some things are just part of the ‘Aether’.

A DEFICIENT number is one whose proper factors sum to less than the number.

(EX) 4 is deficient since proper factors added…1+2 = 3 < 4

An ABUNDANT number is one whose proper factors total more than the number itself.

A PERFECT number is equal to the sum of its factors.

Write the program that will print the numbers 4 to 100 and their type, in a nice little chart.

NUMBER SUM DEF ABUN PERF

4 3 X - -

5 1 X - -

6 6 - - X

7 1 X - -

8 7 X - -

9 4 X - -

10 8 X - -

Have the chart print out 20 numbers at a time, pause for a couple seconds, clear screen, and continue.

Hint: Modify Program 22. Put an outside for loop that goes like this…

for( num=4 ; num<=100 ; ++num) //your number loop

{

sum = 0;

for( y=1 ; y<(num/2) ; ++y) //your factor loop

}