Compatible Numbers Checker

Enter two numbers to determine if they are compatible.

Compatible Numbers Check

Result

What Are Compatible Numbers?

Compatible numbers are a pair of numbers, N and M, that satisfy the following conditions:

Each number has a divisor, dN for N and dM for M.
Subtracting dN from the sum of N's divisors (excluding N itself and dN) equals M.
Similarly, subtracting dM from the sum of M's divisors (excluding M itself and dM) equals N.

How to Determine If Two Numbers Are Compatible

Find the Proper Divisors: Calculate all divisors of each number, excluding the number itself.
Test for dN and dM: Iterate through the divisors to find values of dN and dM that satisfy the conditions.
Check Results: If both N - dN = M and M - dM = N hold true, the numbers are compatible. Otherwise, they are not compatible.

Examples

Example 1: Are 24 and 28 compatible?

Solution:

Divisors of 24 (excluding itself):

1, 2, 3, 4, 6, 8, 12

Testing dN:

dN = 4: 1 + 2 + 3 + 6 + 8 + 12 - 4 = 28

Divisors of 28 (excluding itself):

1, 2, 4, 7, 14

Testing dM:

dM = 2: 1 + 4 + 7 + 14 - 2 = 24

Conclusion: 24 and 28 are compatible numbers.

Example 2: Are 80 and 104 compatible?

Solution:

Divisors of 80 (excluding itself):

1, 2, 4, 5, 8, 10, 16, 20, 40

Testing dN:

dN = 1: 2 + 4 + 5 + 8 + 10 + 16 + 20 + 40 - 1 = 104

Divisors of 104 (excluding itself):

1, 2, 4, 8, 13, 26, 52

Testing dM:

dM = 13: 1 + 2 + 4 + 8 + 26 + 52 - 13 = 80

Conclusion: 80 and 104 are compatible numbers.

Example 3: Are 10 and 14 compatible?

Solution:

Divisors of 10 (excluding itself):

1, 2, 5

Testing dN:

No dN satisfies the conditions since 1 + 2 + 5 = 8 < 14.

Conclusion: 10 and 14 are not compatible numbers.

Compatible Numbers Checker

Compatible Numbers Check

Result

What Are Compatible Numbers?

How to Determine If Two Numbers Are Compatible

Examples

Example 1: Are 24 and 28 compatible?

Example 2: Are 80 and 104 compatible?

Example 3: Are 10 and 14 compatible?

Latest Calculators

Most Popular Calculators