FRIENDLY NUMBER

                                                                      FRIENDLY NUMBERS

FRIENDLY NUMBER is different from Friend / Amicable Numbers. So don't get confused with its similarity.

Friendly Number

Two or more natural numbers are called friendly numbers if they have common abundancy index. The common abundancy index is decided by dividing the sum of all divisors of a number including itself by the number itself.

Example:- 30 has the divisors – 1, 2, 3, 5, 6, 10, 15 and 30

The sum of divisors = 1 + 2 + 3 + 5 + 6 + 10 + 15 + 30 = 72

Abundancy index = 72/30 = 12/5

The abundancy index of a number could be a natural number or rational number.

If the sum of divisors of a number  (excluding itself) = Number itself , it is called Perfect Number

If the sum of divisors of a number  (excluding itself) >Number itself , it is called Abundant Number

If the sum of divisors of a number  (excluding itself) < Number itself , it is called Deficient Number

6 and 28 are Perfect Numbers

Divisor of 6 = 1, 2 and 3 . Sum of divisors = 1 + 2 + 3 = 6

Divisors of 28 are = 1, 2, 4 ,7 and 14 . Sum of divisors = 1 + 2 + 4 + 7 + 14 = 28

6 and 28 are friendly number with abundancy index 2, i.e. any number with abundancy index 2 is called Friendly numbers.

Divisors of 6 = 1, 2, 3 and 6

Sum of Divisors = 1 + 2 + 3 + 6 = 12

Abundancy Index = 12 /6 = 2

Divisor of 28 = 1, 2, 4, 7, 14 and 28

Sum of divisors = 1 + 2 + 4 + 7 + 14 + 28 = 56

Abundancy Index = 56 / 28 = 2

Since 6 and 28 have same abundancy index so they are FRIENDLY NUMBERS.

More examples of friendly numbers are --- (30,140) (2480, 6200 and 40640)

 If you want to know about Amicable/Friends Number 

FRIEND NUMBER/ AMICABLE NUMBERS

READ ANOTHER ARTICLE 

Numbers with Cool Names: Amicable, Sociable, Friendly – TOM ROCKS MATHS

LIST OF DIFFERENT NUMBERS

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DR RAJESH KUMAR THAKUR