Math Problem Solver

Each task must be in seperate methods

$($at least $9)$

Please write in java

DO NOT USE BREAK STATEMENTS!

Introduction:

This is a menu driven program that leverages different methods. The choices are:

Decide if the three numbers given by the user are a Pythagorean Triplet.

isPythagoreanTriplet$($int$,$ int, int$)$

Decide if a number given by the user is a prime number.

isPrimeNumber$($int$)$

Display the factor$-$pairs of a number provided by the user.

showFactors$($int$)$

Display the greatest common factor $($GCF$)$ of two numbers provided by the user.

greatestCommonFactor$($int$,$ int$)$

Display the proper$-$divisors of a number provided by the user.

properDivisor$($int$)$

Observe that proper divisors exclude the 'host number'; for example, the proper divisors of $6$ are $\{1,2,3\}.$

Observe that proper divisors do not repeat divisors in a perfect square; proper divisors are not factor$-$pairs. For example, the proper divisors of $25$ are $\{1,5\}.$

Decide if a number entered by the user is a Perfect Number, Abundant Number, or Deficient Number.

isPerfectNumber$($int$)$

Decide if two numbers entered by the user are Amicable Numbers.

areAmicable$($int$,$ int$)$

Display the prime factors of a number entered by the user.

primeFactors$($int$)$

Display the least common multiple $($LCM$)$ of two numbers using the prime factors entered by the user

leastCommonMultiple$($int$,$ int$)$

Observe that credit will not be awarded unless prime factors are used to compute the least common multiple $($LCM$).$

The following resources demonstrate the process of calculating the: Video #$1,$ Video #$2.$ Webpage #$1,$ and Webpage #$2.$