Coding Stories: Exploring Factors

Greg Benedis-Grab
Jun 2 · 12 min read

Look at each number { 1,2,3,4,5.... n }
For each of the above #'s look at the the #'s {1 to that number
Check if the second number divides into the first number evenly
For each of the first numbers report the count of even divisions (factors)
OUTPUT:
2 has 2 factors.
3 has 2 factors.
4 has 3 factors.
for j in range(2,i//2+1)
Declare variables max_count=0 and max_factors=0.
In the loop check if count is greater than max_count
If it is greater then store max_count and the number in max_factors.
OUTPUT:
The following numbers in the set { 1, . . . 100 } have the most factors
60 with 10 factors
72 with 10 factors
84 with 10 factors
90 with 10 factors
96 with 10 factors
Sieve of of Eratosthenes

60=2²⋅3¹⋅5¹

[2,1,1]=2²⋅3¹⋅5¹=60

OUTPUT:
the prime factorization [2, 1, 1] has a value of 60
the prime factorization [2, 1, 1] has 12 factors
the prime factorization [2, 1, 1] should be written, 2^2*3^1*5^1
OUTPUT:
840 has 32 factors pf: [3, 1, 1, 1, 0, 0, 0, 0, 0]
900 has 27 factors pf: [2, 2, 2, 0, 0, 0, 0, 0, 0]
720 has 30 factors pf: [4, 2, 1, 0, 0, 0, 0, 0, 0]
960 has 28 factors pf: [6, 1, 1, 0, 0, 0, 0, 0, 0]
864 has 24 factors pf: [5, 3, 0, 0, 0, 0, 0, 0, 0]
576 has 21 factors pf: [6, 2, 0, 0, 0, 0, 0, 0, 0]
768 has 18 factors pf: [8, 1, 0, 0, 0, 0, 0, 0, 0]
512 has 10 factors pf: [9, 0, 0, 0, 0, 0, 0, 0, 0]
Highly Composite Numbers on Wikipedia

Greg Benedis-Grab

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exploring the intersection of coding, education and disciplinary knowledge

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