Enter two numbers to determine if they are betrothed.
Betrothed numbers are a pair of positive integers where the sum of the proper divisors of one number (excluding 1 and itself) equals the other number, and vice versa. Unlike amicable numbers, which exclude only the number itself, betrothed numbers also exclude 1.
Solution:
1. Find the Divisors:
Divisors of 60 (excluding 1 and itself): 2, 3, 4, 5, 6, 10, 12, 15, 20, 30
Divisors of 80 (excluding 1 and itself): 2, 4, 5, 8, 10, 16, 20, 40
2. Sum the Divisors:
Sum of Divisors of 60: 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 30 = 107
Sum of Divisors of 80: 2 + 4 + 5 + 8 + 10 + 16 + 20 + 40 = 105
Conclusion: 60 and 80 are not betrothed numbers.
Solution:
1. Find the Divisors:
Divisors of 140 (excluding 1 and itself): 2, 4, 5, 7, 10, 14, 20, 28, 35, 70
Divisors of 195 (excluding 1 and itself): 3, 5, 13, 15, 39, 65
2. Sum the Divisors:
Sum of Divisors of 140: 2 + 4 + 5 + 7 + 10 + 14 + 20 + 28 + 35 + 70 = 195
Sum of Divisors of 195: 3 + 5 + 13 + 15 + 39 + 65 = 140
Conclusion: 140 and 195 are betrothed numbers.
Solution:
1. Find the Divisors:
Divisors of 1050 (excluding 1 and itself): 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525
Divisors of 1925 (excluding 1 and itself): 5, 7, 11, 25, 35, 55, 77, 175, 275, 385
2. Sum the Divisors:
Sum of Divisors of 1050: 2 + 3 + 5 + 6 + 7 + 10 + 14 + 15 + 21 + 25 + 30 + 35 + 42 + 50 + 70 + 75 + 105 + 150 + 175 + 210 + 350 + 525 = 1925
Sum of Divisors of 1925: 5 + 7 + 11 + 25 + 35 + 55 + 77 + 175 + 275 + 385 = 1050
Conclusion: 1050 and 1925 are betrothed numbers.