Overview

In this lab students will build three functions. The first function will calculate the nth Fibonacol number. The second function will check whether a given number is prime. The third function will print the prime factors of a given number. The lab is designed to give students an opportunity to experiment with writing functions while practicing loops and conditionals.

Submission

Your submission should be a single file containing all $3$ functions and no other code. The file name should be your initials, followed by $"\_$Lab$4.$py$".$ For example, "axa$\_$Lab$4.$py$"$

Specification

Function $1$: Fibonacci Numbers

Background

The Fibonacci numbers are a sequence of numbers where each number is the sum of the two numbers that appear before it$.$ The sequence starts with $0$ and $1.$ The first $20$ numbers are as follows: $0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181$

Assignment

Your task is to define a function named "fibonace" that takes an integer and returns the Fibonacci number at that position in the sequence. The number in the first position is $0.$ You can assume that the parameters to the function will be positive integers. You may not use a direct mathematical formula to find the Nth Fibonacci number.

Examples

You can test your function's correctness by checking that all the cases below are true:

fibonacci$(1)=0$

fibonacci$(2)=1$

fibonacci$(3)=**1$

fibonacci$(6)=5$

fibonacci$(25)=46468$

Function $2$: Prime Numbers

Background

A prime number is an integer greater than one that is only divisible by $1$ and itself. You can check if $N$ is divisible by $M$ with the statement $N\%M=0.$ Examples of prime numbers are $2,3,11,$ and $29.$

Examples of non$-$prime numbers are $6,8,$ and $9,6$ and $8$ are divisible by $2\mathrm{.}9$ and $6$ are divisible by $3.$

Assignment

Your task is to define a function named $"$is$\_$prime" that takes an integer as a parameter and returns True if the number is prime, and false if the number is not prime. You can assume that the parameters to the function will be integers, but they may be negative.

Examples

You can test your function's correctness by checking that all the cases below are true:

is$\_$prime$(2)=-$ True

is$\_$prime$(11)=-$ True

is$\_$prime $(1741)=0$ True

is$\_$prime$(1)=-$ False

is$\_$prime$(9)=-$ False

is$\_$prime$(-2)=-$ False

Function $3$: Prime Factorization

Background

All positive integers greater than $1$ can be expressed as the product of a unique combination of prime numbers. This combination of prime numbers is referred to as the number's prime factorization. For example, the number $30$ can be expressed as $2*3*5.$ The prime factorization for a prime number is just itself.

Assignment

Your assignment is to write a function named "print$\_$prime$\_$factors" that will take an integer as its parameter and calculate the integer's prime factorization. While the first two functions returned their results, this function will instead print the result and return nothing. The output should be in the format parameter $=$ factor $1^{**}$ factor $2^{**}$ factor $3.$ Note that a prime may appear more than once in the prime factorization, and the factors should be printed in order of least to greatest.

Examples

Here is a sample program for testing your function:

print$\_$prime$\_$factors$(10)$

print$\_$prime$\_$factors$(2)$

print$\_$prime$\_$factors$(24)$

print$\_$prime$\_$factors$(2475)$

print$\_$prime$\_$factors$(23)$

This should print out the following:

$10=2*5$

$2=2$

$24=2*2*2*3$

$2475=3*3*5*5*11$

$23=23$