Number of Common Factors
This problem is asking us to find the common factors between two given integers, a
and b
. A factor of a number is an integer that can divide the number without leaving a remainder. The common factors of two numbers are the factors that both numbers have in common.
The solution involves a function that calculates the factors of a number, and then finds the common factors between a
and b
:


This code defines a helper function factors
that finds all factors of a given number n
by looping over all integers from 1
to n
and checking if n
is divisible by the integer. It then finds the common factors of a
and b
by getting the intersection of the sets of their factors. The function returns the number of common factors.


This function calculates the number of common factors of two integers a
and b
.
Here’s how it works:
It starts by setting the variable
res
to 1. This is because 1 is a factor of every number.It calculates the greatest common divisor (gcd) of
a
andb
and assigns it tohi
. The gcd is the highest number that can potentially be a common factor ofa
andb
.It then enters a loop that iterates over every number from 2 to
hi
(inclusive).Inside the loop, it checks whether the current number
n
is a factor of botha
andb
(i.e.,a
andb
are both divisible byn
with no remainder). If so, it incrementsres
.Finally, it returns
res
, which is the total number of common factors ofa
andb
.
This function has a time complexity of O(n), where n is the gcd of a
and b
, and a space complexity of O(1), as it only creates a constant number of variables and doesn’t use any data structures that grow with the size of the input.

