Lab
Simple Algorithms

Goal
To explore various algorithms for solving problems using the built-in simple types in C++

1. Use only the four simple types: String, Integer, Double, Boolean
2. Do not use any functions in java.math;
3. Verify your work with a menu-driven program ("`simple.java`") from your teacher.

1. Write a function `factors (Integer num)` that will print all the factors of a given positive integer. For example, factors (30) should produce the following formatted output (note that a period terminates the list):
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
2. Write a function `GCD(Integer a, Integer b)` that returns the greatest common divisor of its two positive integer parameters.
3. Write a Boolean function `prime(Integer num)` that determines whether a given integer greater than one is a prime number. Use this header:
`Boolean prime(Integer num)`
4. Write a function `Double power (Double base, Integer exponent)` that raises a given number (floating point or integer) to a given (positive, negative, or zero) integer power. Do NOT use `pow (x)` or `log (x)` in your solution. Note that if the base is zero, the exponent must be positive.
5. Write a function `findDigit (Integer num, Integer n)` that returns the nth digit from the right of a given integer where n is a positive integer. For example,
`findDigit (30568,2)` will return 6
`findDigit(234,5)` will return 0
`findDigit(-4532,3)` will return 5
6. Write a procedure `downDigits(Integer num)` that will list the digits of a positive integer in one column. For Example:
`downDigits (560)` will produce this output:
```The digits of 560 are: 5 6 0```

Bonus!
Write a function `countDigits (Double num)` that returns the number of digits to the left of the decimal point of a valid floating point number. Note that `countDigits (0.74) returns 1.`

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