Friendly Numbers Calculator

The Friendly Numbers Calculator is a free online tool used to check if two numbers are friendly numbers.

Friendly Numbers Calculator

Eg, Are 80 and 200 friendly numbers? Enter 80 into the first input box and enter 200 into the second input box.

What is a friendly number?

A friendly number is a pair of positive integers in which the ratio of the sum of the factors of one number to itself is equal to the ratio of the sum of the factors of the other integer to itself. For example, if two positive integers A and B are friendship numbers, then the formula is

σ(A)A = σ(B)B

where σ(A) is the factor function and represents the sum of all factors of A. σ(B) also has the same meaning.

How to check if two integers are friendly numbers?

By definition, we can know that to judge whether two numbers are friendly numbers, several steps must be taken

1Find all factors of the number.
2Calculate the sum of all factors.
3Calculate the ratio of the sum to the number.
4Determine if two ratios are equal.

For example, are 6 and 28 friendly numbers?

First, calculate all the factors of 6 and 28.

The factors of 6 are 1, 2, 3 and 6.

The factors of 28 are 1, 2, 4, 7, 14 and 28.

Second, calculate the sum of all factors of 6 and 28.

The sum of the factors of 6 is 1 + 2 + 3 + 6 = 12.

The sum of the factors of 28 is 1 + 2 + 4 + 7 + 14 + 28 = 56.

Third, calculate two ratios

The ratio of 6 is 126 = 2.

The ratio of 28 is 5628 = 2.

Finally, compare the ratios.

Obviously, the above two ratios are equal. So, 6 and 28 are friendly numbers.

How to use the friendly numbers calculator

The procedure to use the friendly numbers calculator is as follows:

1Enter 2 positive integers in the two input boxes respectively.
2Click Calculate button to check whether the input numbers are friendly numbers.
3Click the Reset button to start a new verification.

Solved examples using the friendly numbers calculator

Example 1: Are 24 and 46 friendly numbers?

Enter 24 into the first input box.

Enter 46 into the second input box.

Then click Calculate button, as shown in the figure, 24 and 46 are not friendly numbers.

σ(24)24

= 1 + 2 + 3 + 4 + 6 + 8 + 12 + 2424

= 6024

= 52

σ(46)46

= 1 + 2 + 23 + 4646

= 7246

= 3623

Their ratios are not equal.

Example 2: Are 220 and 284 friendly numbers?

Enter 220 into the first input box.

Enter 284 into the second input box.

Then click Calculate button, as shown in the figure, 220 and 284 are not friendly numbers.

σ(220)220

= 1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 + 220220

= 504220

= 12655

σ(284)284

= 1 + 2 + 4 + 71 + 142 + 284284

= 504284

= 12671

Their ratios are not equal.

Friendly Numbers Calculator