Questions tagged [factoring]
This tag describes challenges related to factoring numbers and polynomials. Not related to the Factor programming language.
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 ...
Carryless multiplication is an operation similar to binary long multiplication, but with XOR instead of addition: ...
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 =...
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 ...
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. ...
"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)(...
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 ...
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 ...
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 ...
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.....
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 ...
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 ...
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-...
Generate some rough numbers
Background A number n can be described as B-rough if all of the prime factors of n strictly ...
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\$ ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
Largest Prime Exponents
Given an integer n >= 2, output the largest exponent in its prime factorization. This is OEIS sequence A051903. Example Let ...
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 ...
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 ...
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 <...
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 ...
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 ...
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 ...
Prime factors buddies
Given an integer N > 1, output all other numbers which prime decompositions have the same digits as the prime decomposition of ...
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 ...
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 ...
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 ...
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 ...
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 ...
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. ...
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 ...
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 ...