Question

Use python for programming the fundamental theorem of arithmetic (single factorization theorem), which affirms that every positive integer greater than 1 is a prime number or a single product of prime numbers.

Show the factors in a list and show a dictionary where the keys are the factors of the number entered and the values are how many times each factor appears in the unique combination.

Answer 1

#Python program

import math

def primeFactors(n):
    dist = {}
    while n % 2 == 0:
        if 2 in dist:
            dist[2] = dist[2] + 1
        else:
            dist[2] = 1
        n = n / 2
        
    for i in range(3,int(math.sqrt(n))+1,2):
        while n % i== 0:
            if i in dist:
                dist[i] = dist[i] + 1
            else:
                dist[i] = 1
          
            n = n / i
            
    if n > 2:
        if n in dist:
                dist[n] = dist[n] + 1
        else:
            dist[n] = 1

    return dist

dic = primeFactors(100)

for i in dic:
    print(i , ' = ', dic[i])

#Screenshot

Run Options Window Help File Edit Format import math def prime Factors (n): dist = {} while n x 2 == 0: if 2 in dist: dist[2] = dist[2] + 1 else: dist[2] = 1 n = n / 2 for i in range (3, int (math.sqrt (n)) +1,2): while n i== 0: if i in dist: dist[i] = dist[i] + 1 else: dist[i] = 1 n = n/ i if n > 2: if n in dist: dist[n] else: dist[n] = 1 dist[n] + 1 return dist dic = primeFactors (100) for i in dic: print (i, ', dic[i])