Explain the prime factorization function in Python, pg 87. How is this an example of induction? How are ordinary mathematical induction, strong mathematical induction, and the well-ordering principle for the integers related? from math import sqrtdef prime_factorization (n):# verify that the input is an integer > 2if not isinstance (n,int): return ([])if n<2: return([])factors=[]while n % 2 == 0:# remove factor s of 2factors.append (2)n = n// 2for i in range (3, int (sqrt (n) ) +1,2): # odd factorswhile n % i==0:factors.append (i)n = n // iif n > 2:factors.append (n)return factorsTo see how it works, we try the following factorizations:printprintprint(prime_factorization (123456789))(prime_factorization (333))(prime_factorization (360))[3, 3, 3607, 3803][3, 3, 37][2, 2, 2, 3, 3, 5]87Ch. 10. Induction

prime_factorization function: - This function first verifies input parameter n. If n is not an…

Answered: from math import sqrt def…

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Explain the prime factorization function in Python, pg 87. How is this an example of induction? How are ordinary mathematical induction, strong mathematical induction, and the well-ordering principle for the integers related?

from math import sqrt
def prime_factorization (n):
# verify that the input is an integer > 2
if not isinstance (n,int): return ([])
if n<2: return([])
factors=[]
while n % 2 == 0:
# remove factor s of 2
factors.append (2)
n = n// 2
for i in range (3, int (sqrt (n) ) +1,2): # odd factors
while n % i==0:
factors.append (i)
n = n // i
if n > 2:
factors.append (n)
return factors
To see how it works, we try the following factorizations:
print
print
print
(prime_factorization (123456789))
(prime_factorization (333))
(prime_factorization (360))
[3, 3, 3607, 3803]
[3, 3, 37]
[2, 2, 2, 3, 3, 5]
87
Ch. 10. Induction

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