Are 1184 and 1210 amicable numbers?
Are 1184 and 1210 amicable numbers?
Now, proper divisors of number 1184 are 1, 2, 4, 8, 16, 32, 37, 74, 148, 269, 592 and similarly proper divisors of 1210 are 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605. Hence, numbers 1184 and 1210 are amicable numbers.
How do you prove that two numbers are amicable?
…“amicable numbers”: two numbers are amicable if each is equal to the sum of the proper divisors of the other (for example, 220 and 284). Attributing virtues such as friendship and justice to numbers was characteristic of the Pythagoreans at all times.
How do I find an amicable number?
Steps to Find Amicable Number
- Read or initialize two numbers (N1, N2) from the user.
- Find the divisor (divOfN1, divOfN2) of both numbers.
- Find the sum of divisors (sumdiv1, sumdiv2) of both numbers.
- Check if the sum of divisors of one number is equal to the other number or not. If equal, the pair of numbers is amicable.
Are 2620 and 2924 amicable numbers?
For example, consider amicable pair (2620, 2924), where 2620 is divisible by 2+6+2+0 = 10 (i.e. 2620/10 = 262) and 2924 is divisible by 2+9+2+4 = 17 (i.e. 2924/17 = 172). So both 2620 and 2924 are Harshad numbers and hence the Amicable Pair (2620, 2924) is Harshad Amicable Pair.
Are 5020 and 5564 amicable numbers?
The first few amicable pairs are (220, 284), (1184, 1210), (2620, 2924), (5020, 5564), (6232, 6368), (10744, 10856), (12285, 14595), (17296, 18416), and (63020, 76084). There are 5,001 amicable pairs in which each number is less than 3.06 x 1011.
Why did Ramanujan say 220 and 284?
Mathematician Ramanujan didn’t have any close friends – someone asked him the reason. He replied that although he wanted to have close friends – nobody was up to his expectation. When pressed how he expected his friends to be – he replied – like numbers 220 and 284.
Are 60 and 84 amicable numbers?
Amicable Numbers The Greeks considered the pair of numbers 220 and 284 to be amicable or friendly numbers because the sum of the proper divisors of one of the numbers is the other number. a. 60 and 84 are amicable numbers.
What is the Speciality in number 220 and 284?
The smallest pair of amicable numbers is (220, 284). They are amicable because the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220.
What are the proper divisors of 220?
They are amicable because the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220.
What is Hardy-Ramanujan number what is the story behind this number?
1729, the Hardy-Ramanujan Number, is the smallest number which can be expressed as the sum of two different cubes in two different ways. 1729 is the sum of the cubes of 10 and 9 – cube of 10 is 1000 and cube of 9 is 729; adding the two numbers results in 1729.
What are the factors of 284?
The factors of 284 are 1, 2, 4, 71, 142, 284. Therefore, 284 has 6 factors.