Suppose we have a number N, we have to find all factors of N and return the product of four factors of N such that: The sum of the four factors is same as N. The product of the four factors is maximum. All four factors can be equal to each other to maximize the product.
So, if the input is like N = 60, then the output will be All the factors are -> 1 2 3 4 5 6 10 12 15 20 30 60 and product is 50625, as we 15 has been selected four times to make product largest.
To solve this, we will follow these steps −
factors := a new list
for i in range 1 to integer of (square root of n) + 1, do
if n mod i is same as 0, then
insert i at the end of factors
insert integer of (n / i) at the end of factors
sort the list factors
display factors
final_prod := 1, flag := 1
for i in range 0 to size of factors, do
for j in range i to size of factors, do
for k in range j to size of factors, do
y := n - factors[i] - factors[j] - factors[k]
if y <= 0, then
come out from the loop
if n mod y is same as 0, then
flag := 0
final_prod := maximum of factors[i] * factors[j] * factors[k] * y, final_prod
if flag is same as 0, then
display final_prod
otherwise,
display "Not possible"
Example
Let us see the following implementation to get better understanding −
from math import *
def get_factors(n) :
factors = []
for i in range(1, int(sqrt(n)) + 1) :
if n % i == 0 :
factors.append(i)
factors.append(n // i)
factors.sort()
print("Factors are ", factors)
final_prod = 1
flag = 1
for i in range(0, len(factors)) :
for j in range(i, len(factors)) :
for k in range(j, len(factors)) :
y = n - factors[i] - factors[j] - factors[k]
if y <= 0 :
break
if n % y == 0 :
flag = 0
final_prod = max(factors[i] * factors[j] * factors[k] * y , final_prod)
if flag == 0 :
print("Product is", final_prod)
else :
print("Not possible")
n = 60
get_factors(n)Input
60
Output
Factors are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60] Product is 50625