Questions tagged [factoring]
This tag describes challenges related to factoring numbers and polynomials. Not related to the Factor programming language.
39
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Random factorized numbers
Input
The code should take an integer \$n\$ between 1 and 1000.
Output
The code should output positive integers with \$n\$ bits. Accompanying each integer should be its full factorization. Each ...
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25
answers
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Find the Prime Signature
The Prime Signature of a number is the list of the exponents of the prime factors of a number, sorted in descending order (exponents of 0 are ignored). Inspired by ...
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11
answers
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Carryless factors
Carryless multiplication is an operation similar to binary long multiplication, but with XOR instead of addition:
...
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12
votes
7
answers
814
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Prime Factorization - but on the exponents too
Though there is a prime factorization challenge and it's here, this, I feel, will be a bit more interesting than that one.
To understand this, let's have an example; I will use 5,184 for this. \$5184 =...
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Prime Factorization [duplicate]
Although there was a prime factors challenge posted ten years ago, it has tedious I/O and restricted time. In this challenge, your task is to write a program or function which takes an integer \$n \ge ...
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9
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8
answers
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Squarefree Palindromes [closed]
Create the shortest function, program, or expression that calculates a sequence of squarefree palindromic numbers.
A squarefree number is one which is not evenly divisible by a square number (i.e. ...
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28
answers
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"Factorise" a quadratic [duplicate]
When learning to factorise quadratics in the form \$x^2 + ax + b\$, a common technique is to find two numbers, \$p, q\$ such that
$$pq = b \\
p + q = a$$
as, for such numbers, \$x^2 + ax + b = (x + p)(...
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32
votes
20
answers
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Looks prime to me!
Figuring out whether a given number is prime, while not very complicated, is kind of hard. But making a guess doesn't need to be.
Seeing whether a number is a multiple of 2 or 5 is easy - you can just ...
- 3,755
-7
votes
1
answer
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No. Of Factors Does the Number Have [duplicate]
Create a function which takes in a input integer and then returns the number of factors it has, like if you pass 25 then it will return ...
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11
answers
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Output Distinct Factor Cuboids
Output Distinct Factor Cuboids
Today's task is very simple: given a positive integer, output a representative of each cuboid formable by its factors.
Explanations
A cuboid's volume is the product ...
- 32.3k
29
votes
18
answers
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Infinitely many primes
Since Euclid, we have known that there are infinitely many primes. The argument is by contradiction: If there are only finitely many, let's say \$p_1,p_2,...,p_n\$, then surely \$m:=p_1\cdot p_2\cdot.....
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9
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Fastest way to iterate over sublattice of discrete lattice
I need to construct a functor that iterates over the linear representation of a sub-lattice of size \$d_x,d_y,d_z,d_q\$ embedded in a lattice of size \$n_x,n_y,n_z,n_q\$. The sub-lattice corner is ...
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2
votes
1
answer
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Find all diagonal counts in only one direction [closed]
If I need to get the number of diagonal squares in all directions:
I do the following formula 2 N − 2 − |x − y| − |x + y − N − 1|
The above example has 13 and ...
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votes
66
answers
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Am I not good enough for you?
Background:
The current Perfect Numbers challenge is rather flawed and complicated, since it asks you to output in a complex format involving the factors of the number. This is a purely decision-...
- 47.1k
16
votes
12
answers
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views
Generate some rough numbers
Background
A number n can be described as B-rough if all of the prime factors of n strictly ...
- 11.2k
22
votes
36
answers
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Find the Squarish Root
Write code that when given a positive number \$x\$ as input, outputs the largest positive divisor of \$x\$ less than or equal to the square root of \$x\$.
In other words find the largest \$n > 0\$ ...
- 96.6k
16
votes
10
answers
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Prime Factor Encoding
How the encoding works
Given a list of bits:
Hold a prime (starting with 2)
Have a list
For each bit in the input
If it's the same as the previous bit, add the ...
- 2,353
31
votes
10
answers
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Find the dot product of Rationals
I was at a friend's house for dinner and they suggested the idea of a "Prime-factor vector space". In this space the positive integers are expressed as a vector such that the nth element in the ...
- 96.6k
16
votes
7
answers
670
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Queue Our Decomposition
In this challenge I will ask you to find a QR decomposition of a square matrix. The QR decomposition of matrix A is two Matrices Q and R such that A = QR. In particular we are looking for Q to be an ...
- 96.6k
12
votes
6
answers
371
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Primes ’n’ Digits
This has no practical purpose but it could be fun to golf.
Challenge
Given a number n,
Count the amount of each digit in n and add 1 to each count
Take the prime factorization of n
Count the amount ...
- 1,214
21
votes
5
answers
812
views
Is my number Unique
In this challenge we learned a way to encode every positive integer using factor trees.
Here is how it works:
The empty string has value of 1.
(S) where ...
- 96.6k
20
votes
21
answers
2k
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Determine Superabundance
A superabundant number is an integer n that sets a new upper bound for its ratio with the divisor sum function σ. In other words, n is superabundant if and only if, for all positive integers x ...
- 3,616
13
votes
7
answers
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Encode Factor Trees [duplicate]
I once saw on the xkcd fora a format for expressing numbers in an odd way. In this "factor tree" format:
The empty string is 1.
Concatenation represents multiplication.
A number n enclosed in ...
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22
votes
28
answers
2k
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Largest Prime Exponents
Given an integer n >= 2, output the largest exponent in its prime factorization. This is OEIS sequence A051903.
Example
Let ...
user45941
28
votes
67
answers
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Find the sum of the divisors of N
Write a program that displays on the screen the sum of the divisors of a number (1 ≤ N ≤ 100) entered by the user in the range of 1 to N.
This is OEIS A000203.
Examples:
Input: 7
...
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votes
11
answers
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Encode an integer
Given positive integer n > 2. We convert it to an array as follows:
If it is equal to 2 return an empty array
Otherwise ...
user72349
12
votes
7
answers
548
views
Number of sums of factors
Given a positive integer n > 1 determine how many numbers can be made by adding integers greater than 1 whose product is n. For example if n = 24 we can express n as a product in the following ways
<...
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7
votes
7
answers
529
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Composite Factorization
This is similar to prime factorization, where you find the smallest prime factors of a number (i.e. 8 = 2 x 2 x 2). But this time, you are to return an array/list of the smallest composite factors of ...
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34
votes
45
answers
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Calculate the prime factors
We had a prime factorization challenge a while ago, but that challenge is nearly six years old and barely meets our current requirements, so I believe it's time for a new one.
Challenge
Write a ...
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34
votes
14
answers
1k
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Generate n-ary numbers
A secondary number is a positive integer whose prime factors (without multiplicity) are all less than or equal to its square root. 4 is a secondary number, because ...
user45941
21
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10
answers
2k
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Prime factors buddies
Given an integer N > 1, output all other numbers which prime decompositions have the same digits as the prime decomposition of ...
- 38.4k
14
votes
13
answers
841
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Palindromic Prime Factors
Palindromic prime problems are pretty common, but that's not what this question is about. In this challenge, the number doesn't have to be a palindrome, its prime factors do.
Task
Your code has to ...
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23
votes
21
answers
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Diamond Puzzles!
Explanation:
Last year in math class, on homework we would occasionally get these extremely simple, although equally annoying questions called diamond puzzles. These were basically questions where we ...
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17
answers
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Sums of prime factors
2013 has the prime factorization 3*11*61. 2014 has the prime factorization 2*19*53. An interesting property regarding these ...
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21
votes
9
answers
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Novel Prime Factors of Repunits
The Background
Folks were talking prime factorization in chat and we found ourselves talking about repunits. Repunits are a subset of the numbers known as repdigits, which are numbers consisting of ...
- 43.3k
22
votes
3
answers
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Factoring a 64-bit integer
Write a GOLF assembly program that reads an integer from stdin (followed by a trailing newline), and outputs its prime factors seperated by newlines, followed by a trailing newline on stdout.
The ...
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24
votes
22
answers
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Check if a number is a product of consecutive integer numbers
Some numbers such as: 6, 12, 20, 30, 42, 56, 60, 90, 120 and so on as can be expressed as a product of consecutive integer numbers as shown below.
...
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3
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List prime-factorized natural numbers up to N in ascending order
For a given n list prime factorization of all natural numbers between 1 and n in ascending ...
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votes
26
answers
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Find the prime factors
In this task, you have to write a program, that computes the prime factors of a number. The input is a natural number 1 < n < 2^32. The output is a list of the prime factors of the number in the ...
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