# What is special about the numbers 220 and 284?

## What is special about the numbers 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.

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. Note: A proper divisor of a number is a positive factor of that number other than the number itself.

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.

### Do betrothed numbers exist?

Related. Numbers do exist where the sum of all the divisors σ(n) is equal to 2n + 2: 20, 104, 464, 650, 1952, 130304, 522752 … Betrothed numbers relate to quasiperfect numbers like amicable numbers relate to perfect numbers.

Why did Ramanujan say 220 and 284?

When pressed how he expected his friends to be – he replied – like numbers 220 and 284. Ramanujan explained that an ideal friendship should be like these numbers – to complement each other – even when one is absent – the other should represent the friend!

Are 220 and 284 amicable?

Definition of amicable number Note: 220 and 284 are examples of amicable numbers. The factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110, which sum to 284, while the factors of 284 are 1, 2, 4, 71, and 142, which sum to 220.

#### Why is 220 a special number?

Also, being divisible by the sum of its digits, 220 is a Harshad number. It is the sum of four consecutive primes (47 + 53 + 59 + 61). It is the smallest even number with the property that when represented as a sum of two prime numbers (per Goldbach’s conjecture) both of the primes must be greater than or equal to 23.

What are the factors of 284?

FAQs on Factors of 284 The factors of 284 are 1, 2, 4, 71, 142, 284 and its negative factors are -1, -2, -4, -71, -142, -284.

What numbers dont exist?

There is however fake/non-existent numbers that have made their way into the mathematics community. Negative numbers are fake numbers that do not exist. Negative square roots are fake and don’t exist. Zero is known as an integer when it is not because it is completely irrational so it’s fake as well.

## Why Ramanujan has no close friend?

Mathematician Ramanujam 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 expectations. When pressed how he expected his friend to be – he replied – like numbers 220 and 284! Intelligence alone cannot be a factor for friendship.

What are proper divisors?

A positive proper divisor is a positive divisor of a number , excluding itself. For example, 1, 2, and 3 are positive proper divisors of 6, but 6 itself is not.

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