Exercise 1: (Design of algorithm to find greatest common divisor) In mathematics, the greatest common divisor (gcd) of two or more integers is the largest positive integer that divides each of the integers. For example, the gcd of 8 and 12 is 4. Why? Divisors of 8 are 1, 2, 4, 8. Divisors of 12 are 1, 2, 4, 6, 12 Thus, the common divisors of 8 and 12 are 1, 2, 4. Out of these common divisors, the greatest one is 4. Therefore, the greatest common divisor (gcd) of 8 and 12 is 4. Write a programming code for a function FindGCD(m,n) that find the greatest common divisor. You can use any language of Java/C++/Python/Octave. Find GCD Algorithm: Step 1 Make an array to store common divisors of two integers m, n. Step 2 Check all the integers from 1 to minimun(m,n) whether they divide both m, n. If yes, add it to the array. Step 3 Return the maximum number in the array.

Problem Description: The bird of paradise called the Helipixsal is renowned for its magnificent tail feathers which range in number from five to nine ornate feathers each of a different length. Their "magnificence" is quantified by the rather simple process of counting the exact number of tail feathers and multiplying this by the difference in the length of the minimum and maximum lengths of tail feather. You are to write a simple program that will allow the user to enter the length of each tail feather individually and keep on entering feathers until a -1 is entered. The program will then return the quantified "magnificence" factor.

9: perfect.cpp) A number is called perfect if the sum of its divisors is equal to the original number. A number is called deficient if the sum of its divisors is less than the original number. A number is called abundant if the sum of its divisors is more than the original number. Write a program that answers the following questions: What numbers below 5000 are perfect? What odd numbers below 5000 are abundant? What are the relative proportions of deficient, abundant, and perfect numbers? 5000 should be in a global constant.

(Conversion) a. Write a C++ program to convert meters to feet. The program should request the starting meter value, the number of conversions to be made, and the increment between metric values. The display should have appropriate headings and list the meters and the corresponding feet value. If the number of iterations is greater than 10, have your program substitute a default increment of 10. Use the relationship that 1 meter = 3.281 feet. b. Run the program written in Exercise 6a on a computer. Verify that your program begins at the correct starting meter value and contains the exact number of conversions specified in your input data. c. Modify the program written in Exercise 6a to request the starting meter value, the ending meter value, and the increment. Instead of the condition checking for a fixed count, the condition checks for the ending meter value. If the number of iterations is greater than 20, have your program substitute a default increment of (ending value - starting value) / 19.

15. Write a program to implement and test the algorithm that you designed for Exercise 15 of Chapter 1. (You may assume that the value of . In your program, declare a named constant PI to store this value.)

C language program

Python 6. Sum of Numbers Design a function that accepts an integer argument and returns the sum of all the integers from 1 up to the number passed as an argument. For example, if 50 is passed as an argument, the function will return the sum of 1, 2, 3, 4, ...50. Use recursion to calculate • the sum.

Please help answer these two questions in Python. (See attached image) Attach screenshots of your code for clarity.

Problem B  Musical Key ConversionThe chromatic scale is a 12-note scale in music in which all notes are evenly spaced: that is, the ratio of the frequency between any two consecutive notes is constant. The notes are typically labeled in the following sequence: A, A#, B, C, C#, D, D#, E, F, F#, G, G# After G#, the labels loop back and start over with A (one octave higher). To convert between musical keys, you can shift all notes in a piece of music a constant number of steps along the scale above. For example, the sequence of notes E, E, F, G, G, F, E, D, C, C, D, E, E, D, D can be converted to another musical key by shifting everything up three steps: E, E, F, G, G, F, E, D, C, C, D, E, E, D, D G, G, G#, A#, A#, G#, G, F, D#, D#, F, G, G, F, F Notice that G was converted to A#, since going three steps up required us to loop off of the top of the scale back to the bottom: G -> G# -> A -> A#. Technically we should note that this would be A# of the next octave up, but we’ll…