Given an integer . The task is to find all factors of N print the product of four factors of N such that:
- Sum of the four factors is equal to N.
- Product of the four factors is maximum.
If it is not possible to find 4 such factors then print “Not possible”.
Note: All the four factors can be equal to each other to maximize the product.
Input : 24 Output : Product -> 1296 All factors are -> 1 2 3 4 6 8 12 24 Choose the factor 6 four times, Therefore, 6+6+6+6 = 24 and product is maximum. Input : 100 Output : Product -> 390625 All the factors are -> 1 2 4 5 10 10 20 25 50 100 Choose the factor 25 four times.
In the second example, the product will be maximum when the four factors will be equal to 25. The sum of four factors is equal to ‘N’. Though we can choose the same factor four times to maximize the product.
Below is the step by step algorithm to solve this problem:
- First find the factors of a number ‘N’ by traversing from 1 to square root of ‘N’ and check if ‘i’ and ‘n/i’ divides N and store them in a vector.
- Sort the vector and print every element.
- Find three numbers to maximize the product with the fourth number, using three loops.
- Replace the next maximum product with the previous product.
- Print the product when you’ll find the four factors.
Below is the implementaion of above approach:
All the factors are -> 1 2 5 10 25 50 Product is -> 12500
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- Find four factors of N with maximum product and sum equal to N | Set-2
- Find four factors of N with maximum product and sum equal to N | Set 3
- Maximize the product of four factors of a Number
- Find number of factors of N when location of its two factors whose product is N is given
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- Minimum sum obtained from groups of four elements from the given array
- Find the area of the shaded region formed by the intersection of four semicircles in a square
- Find the prime P using given four integers
- Product of factors of number
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