Program to find number of values factors of two set of numbers

Suppose we have two arrays called nums1 and nums2. We have to find the number of values that satisfy the following conditions:

• The elements in nums1 are the factors of the elements which are being selected

• The elements which are selected are factors of all elements of nums2

So, if the input is like nums1 = [3,9] and nums2 = [27, 81], then the output will be 2 because the numbers are 9 and 27.

Algorithm

To solve this, we will follow these steps:

• count := 0
• For each number i in range 1 to 100:
  • Check if all elements in nums1 divide i evenly
  • Check if i divides all elements in nums2 evenly
  • If both conditions are true, increment count
• Return count

Example

Let us see the following implementation to get better understanding:

def solve(nums1, nums2):
    count = 0
    for i in range(1, 101):
        flag = True
        
        # Check if all elements in nums1 are factors of i
        for j in nums1:
            if i % j != 0:
                flag = False
                break
        
        if flag:
            # Check if i is a factor of all elements in nums2
            for k in nums2:
                if k % i != 0:
                    flag = False
                    break
        
        if flag:
            count += 1
    
    return count

nums1 = [3, 9]
nums2 = [27, 81]
result = solve(nums1, nums2)
print(f"Number of valid values: {result}")

Number of valid values: 2

How It Works

For the example nums1 = [3, 9] and nums2 = [27, 81], the valid numbers are:

• Number 9: 9 % 3 = 0, 9 % 9 = 0, 27 % 9 = 0, 81 % 9 = 0 ?
• Number 27: 27 % 3 = 0, 27 % 9 = 0, 27 % 27 = 0, 81 % 27 = 0 ?

Complete Example with Verification

def solve(nums1, nums2):
    count = 0
    valid_numbers = []
    
    for i in range(1, 101):
        flag = True
        
        # Check if all elements in nums1 are factors of i
        for j in nums1:
            if i % j != 0:
                flag = False
                break
        
        if flag:
            # Check if i is a factor of all elements in nums2
            for k in nums2:
                if k % i != 0:
                    flag = False
                    break
        
        if flag:
            count += 1
            valid_numbers.append(i)
    
    return count, valid_numbers

nums1 = [3, 9]
nums2 = [27, 81]
count, valid = solve(nums1, nums2)

print(f"Count: {count}")
print(f"Valid numbers: {valid}")

Count: 2
Valid numbers: [9, 27]

Conclusion

This algorithm finds numbers that are multiples of all elements in the first array and factors of all elements in the second array. The solution iterates through possible values and checks both conditions for each candidate number.